2
(b) Determine the mean and standard deviation of
x.
Show all work. Just the answer, without supporting work, will
receive no credit
11.Mimi plans make a random guess at 10
trueorfalse questions. Answer the following questions:
(a) Let X be the number of correct answers Mimi gets.
As we know, the distribution of X is a binomial probability
distribution. What is the number of trials (n), probability of
successes (p) and probability of failures (q), respectively?
(b) Find the probability that she gets at most 5
correct answers. (Round the answer to 3 decimal places.
(c) To get the answers for part (b), what technology
did you use? If an online applet was used, list the URL and
describe the steps. If a calculator or Excel was used, write out
the function
12.The heights of pecan trees are normally
distributed with a mean of 10 feet and a standard deviation of 2
feet.
Show all work. Just the answer, without supporting work, will
receive no credit.
(a) What is the probability that a randomly selected
pecan tree is between 9 and 12 feet tall? (round the answer to 4
decimal places)
(b) Find the 75
th percentile of the pecan tree height
distribution. (round the answer to 2 decimal places)
(c) To get the answers for part (a) and part (b),
what technology did you use? If an online applet was used, list the
URL and describe the steps. If a calculator or Excel was used,
write out the function
13.Based on the performance of all individuals who
tested between July 1, 2014 and June 30, 2017, the GRE Verbal
Reasoning scores are normally distributed with a mean of 150.05 and
a standard deviation of 8.43. (
https://www.ets.org/s/gre/pdf/gre_guide_table1a.pdf).
Show all work. Just the answer, without supporting work, will
receive no credit.
(a) Consider all random samples of 36 test scores.
What is the standard deviation of the sample means? (Round your
answer to three decimal places)
(b) What is the probability that 36 randomly selected
test scores will have a mean test score that is between 150 and
155? (Round your answer to four decimal places)
(c) To get the answer for part (b), what technology
did you use? If an online applet was used, list the URL and
describe the steps. If a calculator or Excel was used, write out
the function
14.A survey showed that 1200 of the 1600 adult
respondents believe in global warming.
(a) Construct a 95% confidence interval estimate of
the proportion of adults believing in global warming.
Show all work. Just the answer, without supporting work, will
receive no credit. Include description of how confidence interval
was constructed.
(b) Describe the confidence interval in everyday
language
15.A city built a new parking garage in a business
district. For a random sample of 100 days, daily fees collected
averaged $2,000, with a standard deviation of $500.
(a) Construct a 90% confidence interval estimate of
the mean daily income this parking garage generates.
Show all work. Just the answer, without supporting work, will
receive no credit. Include description of how confidence interval
was constructed.
(b) Describe the confidence interval in everyday
language
16.A researcher claims the proportion of auto
accidents that involve teenage drivers is greater than 10%. ABC
Insurance Company checks police records on 200 randomly selected
auto accidents and notes that teenagers were at the wheel in 25 of
them.
Assume the company wants to use a 0.10 significance
level to test the researcher’s claim.
(a) What is the appropriate hypothesis test to use
for this analysis: onesample ztest for the population proportion,
onesample ttest for population proportion, onesample ztest for
population mean, or onesample t test for population mean? Please
identify and explain why it is appropriate.
(b) Identify the null hypothesis and the alternative
hypothesis.
(c) Determine the test statistic. Round your answer
to two decimal places.
Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
(d) Determine the
Pvalue for this test. Round your answer to three decimal
places.
Show all work; writing the correct Pvalue, without supporting
work, will receive no credit.
(e) Compare pvalue and significance level α. What
decision should be made regarding the null hypothesis (e.g., reject
or fail to reject) and why?
(f) Is there sufficient evidence to support the
researcher’s claim that the proportion of auto accidents that
involve teenage drivers is greater than 10%? Explain
17.Mimi was curious if regular excise really helps
weight loss, hence she decided to perform a hypothesis test. A
random sample of 5 UMUC students was chosen. The students took a
30minute exercise every day for 6 months. The weight was recorded
for each individual before and after the exercise regimen. Does the
data below suggest that the regular exercise helps weight loss?
Assume Mimi wants to use a 0.05 significance level to test the
claim
(a) What is the appropriate hypothesis test to use
for this analysis: ztest for two proportions, ttest for two
proportions, ttest for two dependent samples (matched pairs), or
ttest for two independent samples? Please identify and explain why
it is appropriate.
(b) Let μ
1 = mean weight before the exercise regime. Let μ
2 = mean weight after the exercise regime. Which
of the following statements correctly defines the null hypothesis?
(i) μ
1  μ
2 > 0 (μ
d > 0)
(ii) μ
1  μ
2 = 0 (μ
d = 0)
(iii) μ
1  μ
2 < 0 (μ
d < 0)
(c) Let μ
1 = mean weight before the exercise regime. Let μ
2 = mean weight after the exercise regime. Which
of the following statements correctly defines the alternative
hypothesis?
(a) μ
1  μ
2 > 0 (μ
d > 0)
(b) μ
1  μ
2 = 0 (μ
d = 0)
(c) μ
1  μ
2 < 0 (μ
d < 0)
(d) Determine the test statistic. Round your answer
to three decimal places.
Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
(e) Determine the pvalue. Round your answer to three
decimal places.
Show all work; writing the correct critical value, without
supporting work, will receive no credit.
(f) Compare pvalue and significance level α. What
decision should be made regarding the null hypothesis (e.g., reject
or fail to reject) and why?
(g) Is there sufficient evidence to support the claim
that regular exercise helps weight loss? Justify your conclusion.
18.The UMUC Daily News reported that the color
distribution for plain M&M’s was: 40% brown, 20% yellow, 20%
orange, 10% green, and 10% tan
.Each piece of candy in a random sample of 100
plain M&M’s was classified according to color
,and the results are listed below. Use a 0.05
significance level to test the claim that the published color
distribution is correct.
Show all work and justify your answer.Color

Brown

Yellow

Orange

Green

Tan

Number

42

18

15

7

18
(a) What is the appropriate hypothesis test: ztest
for sample proportion, ttest for sample mean, chisquare goodness
of fit test, Ftest for ANOVA? Please identify and explain why it
is appropriate for analyzing this data.
(b) Identify the null hypothesis and the alternative
hypothesis.
(c) Determine the test statistic. Round your answer
to two decimal places.
Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
(d) Determine the Pvalue. Round your answer to two
decimal places.
Show all work; writing the correct Pvalue, without supporting
work, will receive no credit.
(e) Compare pvalue and significance level α. What
decision should be made regarding the null hypothesis (e.g., reject
or fail to reject) and why?
(f) Is there sufficient evidence to support the claim
that the published color distribution is correct? Justify your
answer
19. A STAT 200 instructor believes that the
average quiz score is a good predictor of final exam score. A
random sample of 10 students produced the following data where
xis the average quiz score and
yis the final exam score.
x

80

95

50

60

100

55

85

70

75

85

y

70

96

50

63

96

60

83

60

77

87
(a) Find an equation of the least squares regression
line. Round the slope and yintercept value to two decimal places.
Describe method for obtaining results. Show all work; writing
the correct equation, without supporting work, will receive no
credit.
(b) Based on the equation from part (a), what is the
predicted final exam score if the average quiz score is 65?
Show all work and justify your answer.
(c) Based on the equation from part (a), what is the
predicted final exam score if the average quiz score is 40? Show
all work and justify your answer.
(d) Which predicted final exam score that you
calculated for (b) and (c) do you think is closer to the true final
exam score and why
20.What is the appropriate statistical analysis to
use: ttest for two independent samples, ttest for dependent
samples, ANOVA, or chisquare test of independence? Please identify
and explain why it is appropriate
(a) A study was conducted to see whether monetary
incentives to use less water during times of drought had an effect
on water usage. Sixty single family homeowners were randomly
assigned to one of two groups: 1) monetary incentives and 2) no
monetary incentives. At the end of three months, the total amount
of water usage for each household, in gallons, was measured.
(b) A study was conducted to see whether the mean
weight loss is the same for 10 different weight loss programs. Each
of the 10 programs had 50 subjects in it. The subjects were
followed for 12 months. Weight change for each subject was recorded
1.The U.S. Census Bureau needs to estimate the
median income of females in the U.S. They collect incomes from 3500
females. Choose the best answer.
Justify for full credit.
(a) Which of the followings is the variable?
(i) Female in the US
(ii) Income of a female in the US
(iii) Set of income responses from all females in the
US
(iv) Median income of set of all females in the US
(b) Which of the followings is the parameter?
(i) Female in the US
(ii) Income of a female in the US
(iii) Set of income responses from all females in the US
(iv) Median income of set of all females in the US
2.Choose the best answer.
Justify for full credit.
(a) The hotel ratings are usually on a scale from 0
star to 5 stars. The level of this measurement is
(i) interval
(ii) nominal
(iii) ordinal
(iv) ratio
(b) In a career readiness research, 100 students were
randomly selected from the psychology program, 150 students were
randomly selected from the communications program, and 120 students
were randomly selected from cyber security program. This type of
sampling is called:
(i) cluster
(ii) convenience
(iii) systematic
(iv) stratified
3. The midterm exam scores in a statistics class are shown
in the following table:
67

92

76

47

85

70

87

76

67

72

84

85

65

82

84

98

81

85

87

83
(a) Complete the following frequency distribution
table using 6 classes: 4049, 5059, 6069, 7079, 8089, and
9099. Express the cumulative relative frequency to two decimal
places. (
Show all work. Just the answer, without supporting work, will
receive no credit.)
(b) What percentage of the midterm exam scores was at
least 70?
4.Answer the following questions based on the
midterm exam score data given in Question # 3
:
(Show all work. Just the answer, without supporting work, will
receive no credit.)
(a) What is the range of the midterm exam scores
?
(b) What is the median of the midterm exam scores?
(c) What is the mode of the midterm exam scores
5.A STAT 200 professor took a sample of 10 midterm
exam scores from a class of 30 students. The 10 scores are shown in
the table below:
95

67

76

47

85

70

87

80

67

72
(a) What is the sample mean?
(b) What is the sample standard deviation? (Round
your answer to two decimal places)
(c) If you leveraged technology to get the answers
for part (a) and/or part (b), what technology did you use? If an
online applet was used, please list the URL, and describe the
steps. If a calculator or Excel was used, please write out the
function
6.There are 4 suits (heart, diamond, clover, and
spade) in a 52card deck, and each suit has 13 cards. Suppose your
experiment is to draw one card from a deck and observe what suit it
is.
Express the probability in fraction format. (
Show all work. Just the answer, without supporting work, will
receive no credit.)
(a) Find the probability of drawing a heart or
diamond.
(b) Find the probability that the card is not a spade
7.There are 2 white balls and 8 red balls in an
urn. Consider selecting one ball at a time from the urn. What is
the probability that the first ball is red and the second ball is
also red? Express the probability in fraction format. (
Show all work. Just the answer, without supporting work, will
receive no credit.)
(a) Assuming the ball selection is with replacement.
(b) Assuming the ball selection is without
replacement
8.
There are twenty stores for a grocery chain in the
MidAtlantic region. The regional executive wants to visit five of
the twenty stores. She asks her assistant to choose five stores and
arrange the visit schedule. (
Show all work. Just the answer, without supporting work, will
receive no credit).
(a) Does the order matter in the scheduling?
(b) Based on your answer to part (a), should you use
permutation or combination to find the different schedules that the
assistant may arrange?
(c) How many different schedules can the assistant
recommend
9.Mimi has seven books from the Statistics is Fun
series. She plans on bringing two of the seven books with her in a
road trip. (
Show all work. Just the answer, without supporting work, will
receive no credit).
(a) Does the order matter in the book selection?
(b) Based on your answer to part (a), should you use
permutation or combination to find the number of the different ways
the two books can be selected?
(c) How many different ways can the two books be
selected
10. Let random variable
xrepresent the number of heads when a fair coin is tossed
two times.
(a) Construct a table describing the probability
distribution.
x

P(x)

0

1

2
(b) Determine the mean and standard deviation of
x.
Show all work. Just the answer, without supporting work, will
receive no credit
11.Mimi plans make a random guess at 10
trueorfalse questions. Answer the following questions:
(a) Let X be the number of correct answers Mimi gets.
As we know, the distribution of X is a binomial probability
distribution. What is the number of trials (n), probability of
successes (p) and probability of failures (q), respectively?
(b) Find the probability that she gets at most 5
correct answers. (Round the answer to 3 decimal places.
(c) To get the answers for part (b), what technology
did you use? If an online applet was used, list the URL and
describe the steps. If a calculator or Excel was used, write out
the function
12.The heights of pecan trees are normally
distributed with a mean of 10 feet and a standard deviation of 2
feet.
Show all work. Just the answer, without supporting work, will
receive no credit.
(a) What is the probability that a randomly selected
pecan tree is between 9 and 12 feet tall? (round the answer to 4
decimal places)
(b) Find the 75
th percentile of the pecan tree height
distribution. (round the answer to 2 decimal places)
(c) To get the answers for part (a) and part (b),
what technology did you use? If an online applet was used, list the
URL and describe the steps. If a calculator or Excel was used,
write out the function
13.Based on the performance of all individuals who
tested between July 1, 2014 and June 30, 2017, the GRE Verbal
Reasoning scores are normally distributed with a mean of 150.05 and
a standard deviation of 8.43. (
https://www.ets.org/s/gre/pdf/gre_guide_table1a.pdf).
Show all work. Just the answer, without supporting work, will
receive no credit.
(a) Consider all random samples of 36 test scores.
What is the standard deviation of the sample means? (Round your
answer to three decimal places)
(b) What is the probability that 36 randomly selected
test scores will have a mean test score that is between 150 and
155? (Round your answer to four decimal places)
(c) To get the answer for part (b), what technology
did you use? If an online applet was used, list the URL and
describe the steps. If a calculator or Excel was used, write out
the function
14.A survey showed that 1200 of the 1600 adult
respondents believe in global warming.
(a) Construct a 95% confidence interval estimate of
the proportion of adults believing in global warming.
Show all work. Just the answer, without supporting work, will
receive no credit. Include description of how confidence interval
was constructed.
(b) Describe the confidence interval in everyday
language
15.A city built a new parking garage in a business
district. For a random sample of 100 days, daily fees collected
averaged $2,000, with a standard deviation of $500.
(a) Construct a 90% confidence interval estimate of
the mean daily income this parking garage generates.
Show all work. Just the answer, without supporting work, will
receive no credit. Include description of how confidence interval
was constructed.
(b) Describe the confidence interval in everyday
language
16.A researcher claims the proportion of auto
accidents that involve teenage drivers is greater than 10%. ABC
Insurance Company checks police records on 200 randomly selected
auto accidents and notes that teenagers were at the wheel in 25 of
them.
Assume the company wants to use a 0.10 significance
level to test the researcher’s claim.
(a) What is the appropriate hypothesis test to use
for this analysis: onesample ztest for the population proportion,
onesample ttest for population proportion, onesample ztest for
population mean, or onesample t test for population mean? Please
identify and explain why it is appropriate.
(b) Identify the null hypothesis and the alternative
hypothesis.
(c) Determine the test statistic. Round your answer
to two decimal places.
Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
(d) Determine the
Pvalue for this test. Round your answer to three decimal
places.
Show all work; writing the correct Pvalue, without supporting
work, will receive no credit.
(e) Compare pvalue and significance level α. What
decision should be made regarding the null hypothesis (e.g., reject
or fail to reject) and why?
(f) Is there sufficient evidence to support the
researcher’s claim that the proportion of auto accidents that
involve teenage drivers is greater than 10%? Explain
17.Mimi was curious if regular excise really helps
weight loss, hence she decided to perform a hypothesis test. A
random sample of 5 UMUC students was chosen. The students took a
30minute exercise every day for 6 months. The weight was recorded
for each individual before and after the exercise regimen. Does the
data below suggest that the regular exercise helps weight loss?
Assume Mimi wants to use a 0.05 significance level to test the
claim
(a) What is the appropriate hypothesis test to use
for this analysis: ztest for two proportions, ttest for two
proportions, ttest for two dependent samples (matched pairs), or
ttest for two independent samples? Please identify and explain why
it is appropriate.
(b) Let μ
1 = mean weight before the exercise regime. Let μ
2 = mean weight after the exercise regime. Which
of the following statements correctly defines the null hypothesis?
(i) μ
1  μ
2 > 0 (μ
d > 0)
(ii) μ
1  μ
2 = 0 (μ
d = 0)
(iii) μ
1  μ
2 < 0 (μ
d < 0)
(c) Let μ
1 = mean weight before the exercise regime. Let μ
2 = mean weight after the exercise regime. Which
of the following statements correctly defines the alternative
hypothesis?
(a) μ
1  μ
2 > 0 (μ
d > 0)
(b) μ
1  μ
2 = 0 (μ
d = 0)
(c) μ
1  μ
2 < 0 (μ
d < 0)
(d) Determine the test statistic. Round your answer
to three decimal places.
Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
(e) Determine the pvalue. Round your answer to three
decimal places.
Show all work; writing the correct critical value, without
supporting work, will receive no credit.
(f) Compare pvalue and significance level α. What
decision should be made regarding the null hypothesis (e.g., reject
or fail to reject) and why?
(g) Is there sufficient evidence to support the claim
that regular exercise helps weight loss? Justify your conclusion.
18.The UMUC Daily News reported that the color
distribution for plain M&M’s was: 40% brown, 20% yellow, 20%
orange, 10% green, and 10% tan
.Each piece of candy in a random sample of 100
plain M&M’s was classified according to color
,and the results are listed below. Use a 0.05
significance level to test the claim that the published color
distribution is correct.
Show all work and justify your answer.Color

Brown

Yellow

Orange

Green

Tan

Number

42

18

15

7

18
(a) What is the appropriate hypothesis test: ztest
for sample proportion, ttest for sample mean, chisquare goodness
of fit test, Ftest for ANOVA? Please identify and explain why it
is appropriate for analyzing this data.
(b) Identify the null hypothesis and the alternative
hypothesis.
(c) Determine the test statistic. Round your answer
to two decimal places.
Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
(d) Determine the Pvalue. Round your answer to two
decimal places.
Show all work; writing the correct Pvalue, without supporting
work, will receive no credit.
(e) Compare pvalue and significance level α. What
decision should be made regarding the null hypothesis (e.g., reject
or fail to reject) and why?
(f) Is there sufficient evidence to support the claim
that the published color distribution is correct? Justify your
answer
19. A STAT 200 instructor believes that the
average quiz score is a good predictor of final exam score. A
random sample of 10 students produced the following data where
xis the average quiz score and
yis the final exam score.
x

80

95

50

60

100

55

85

70

75

85

y

70

96

50

63

96

60

83

60

77

87
(a) Find an equation of the least squares regression
line. Round the slope and yintercept value to two decimal places.
Describe method for obtaining results. Show all work; writing
the correct equation, without supporting work, will receive no
credit.
(b) Based on the equation from part (a), what is the
predicted final exam score if the average quiz score is 65?
Show all work and justify your answer.
(c) Based on the equation from part (a), what is the
predicted final exam score if the average quiz score is 40? Show
all work and justify your answer.
(d) Which predicted final exam score that you
calculated for (b) and (c) do you think is closer to the true final
exam score and why
20.What is the appropriate statistical analysis to
use: ttest for two independent samples, ttest for dependent
samples, ANOVA, or chisquare test of independence? Please identify
and explain why it is appropriate
(a) A study was conducted to see whether monetary
incentives to use less water during times of drought had an effect
on water usage. Sixty single family homeowners were randomly
assigned to one of two groups: 1) monetary incentives and 2) no
monetary incentives. At the end of three months, the total amount
of water usage for each household, in gallons, was measured.
(b) A study was conducted to see whether the mean
weight loss is the same for 10 different weight loss programs. Each
of the 10 programs had 50 subjects in it. The subjects were
followed for 12 months. Weight change for each subject was recorded
1.The U.S. Census Bureau needs to estimate the
median income of females in the U.S. They collect incomes from 3500
females. Choose the best answer.
Justify for full credit.
(a) Which of the followings is the variable?
(i) Female in the US
(ii) Income of a female in the US
(iii) Set of income responses from all females in the
US
(iv) Median income of set of all females in the US
(b) Which of the followings is the parameter?
(i) Female in the US
(ii) Income of a female in the US
(iii) Set of income responses from all females in the US
(iv) Median income of set of all females in the US
2.Choose the best answer.
Justify for full credit.
(a) The hotel ratings are usually on a scale from 0
star to 5 stars. The level of this measurement is
(i) interval
(ii) nominal
(iii) ordinal
(iv) ratio
(b) In a career readiness research, 100 students were
randomly selected from the psychology program, 150 students were
randomly selected from the communications program, and 120 students
were randomly selected from cyber security program. This type of
sampling is called:
(i) cluster
(ii) convenience
(iii) systematic
(iv) stratified
3. The midterm exam scores in a statistics class are shown
in the following table:
67

92

76

47

85

70

87

76

67

72

84

85

65

82

84

98

81

85

87

83
(a) Complete the following frequency distribution
table using 6 classes: 4049, 5059, 6069, 7079, 8089, and
9099. Express the cumulative relative frequency to two decimal
places. (
Show all work. Just the answer, without supporting work, will
receive no credit.)
(b) What percentage of the midterm exam scores was at
least 70?
4.Answer the following questions based on the
midterm exam score data given in Question # 3
:
(Show all work. Just the answer, without supporting work, will
receive no credit.)
(a) What is the range of the midterm exam scores
?
(b) What is the median of the midterm exam scores?
(c) What is the mode of the midterm exam scores
5.A STAT 200 professor took a sample of 10 midterm
exam scores from a class of 30 students. The 10 scores are shown in
the table below:
95

67

76

47

85

70

87

80

67

72
(a) What is the sample mean?
(b) What is the sample standard deviation? (Round
your answer to two decimal places)
(c) If you leveraged technology to get the answers
for part (a) and/or part (b), what technology did you use? If an
online applet was used, please list the URL, and describe the
steps. If a calculator or Excel was used, please write out the
function
6.There are 4 suits (heart, diamond, clover, and
spade) in a 52card deck, and each suit has 13 cards. Suppose your
experiment is to draw one card from a deck and observe what suit it
is.
Express the probability in fraction format. (
Show all work. Just the answer, without supporting work, will
receive no credit.)
(a) Find the probability of drawing a heart or
diamond.
(b) Find the probability that the card is not a spade
7.There are 2 white balls and 8 red balls in an
urn. Consider selecting one ball at a time from the urn. What is
the probability that the first ball is red and the second ball is
also red? Express the probability in fraction format. (
Show all work. Just the answer, without supporting work, will
receive no credit.)
(a) Assuming the ball selection is with replacement.
(b) Assuming the ball selection is without
replacement
8.
There are twenty stores for a grocery chain in the
MidAtlantic region. The regional executive wants to visit five of
the twenty stores. She asks her assistant to choose five stores and
arrange the visit schedule. (
Show all work. Just the answer, without supporting work, will
receive no credit).
(a) Does the order matter in the scheduling?
(b) Based on your answer to part (a), should you use
permutation or combination to find the different schedules that the
assistant may arrange?
(c) How many different schedules can the assistant
recommend
9.Mimi has seven books from the Statistics is Fun
series. She plans on bringing two of the seven books with her in a
road trip. (
Show all work. Just the answer, without supporting work, will
receive no credit).
(a) Does the order matter in the book selection?
(b) Based on your answer to part (a), should you use
permutation or combination to find the number of the different ways
the two books can be selected?
(c) How many different ways can the two books be
selected
10. Let random variable
xrepresent the number of heads when a fair coin is tossed
two times.
(a) Construct a table describing the probability
distribution.
x

P(x)

0

1

2
(b) Determine the mean and standard deviation of
x.
Show all work. Just the answer, without supporting work, will
receive no credit
11.Mimi plans make a random guess at 10
trueorfalse questions. Answer the following questions:
(a) Let X be the number of correct answers Mimi gets.
As we know, the distribution of X is a binomial probability
distribution. What is the number of trials (n), probability of
successes (p) and probability of failures (q), respectively?
(b) Find the probability that she gets at most 5
correct answers. (Round the answer to 3 decimal places.
(c) To get the answers for part (b), what technology
did you use? If an online applet was used, list the URL and
describe the steps. If a calculator or Excel was used, write out
the function
12.The heights of pecan trees are normally
distributed with a mean of 10 feet and a standard deviation of 2
feet.
Show all work. Just the answer, without supporting work, will
receive no credit.
(a) What is the probability that a randomly selected
pecan tree is between 9 and 12 feet tall? (round the answer to 4
decimal places)
(b) Find the 75
th percentile of the pecan tree height
distribution. (round the answer to 2 decimal places)
(c) To get the answers for part (a) and part (b),
what technology did you use? If an online applet was used, list the
URL and describe the steps. If a calculator or Excel was used,
write out the function
13.Based on the performance of all individuals who
tested between July 1, 2014 and June 30, 2017, the GRE Verbal
Reasoning scores are normally distributed with a mean of 150.05 and
a standard deviation of 8.43. (
https://www.ets.org/s/gre/pdf/gre_guide_table1a.pdf).
Show all work. Just the answer, without supporting work, will
receive no credit.
(a) Consider all random samples of 36 test scores.
What is the standard deviation of the sample means? (Round your
answer to three decimal places)
(b) What is the probability that 36 randomly selected
test scores will have a mean test score that is between 150 and
155? (Round your answer to four decimal places)
(c) To get the answer for part (b), what technology
did you use? If an online applet was used, list the URL and
describe the steps. If a calculator or Excel was used, write out
the function
14.A survey showed that 1200 of the 1600 adult
respondents believe in global warming.
(a) Construct a 95% confidence interval estimate of
the proportion of adults believing in global warming.
Show all work. Just the answer, without supporting work, will
receive no credit. Include description of how confidence interval
was constructed.
(b) Describe the confidence interval in everyday
language
15.A city built a new parking garage in a business
district. For a random sample of 100 days, daily fees collected
averaged $2,000, with a standard deviation of $500.
(a) Construct a 90% confidence interval estimate of
the mean daily income this parking garage generates.
Show all work. Just the answer, without supporting work, will
receive no credit. Include description of how confidence interval
was constructed.
(b) Describe the confidence interval in everyday
language
16.A researcher claims the proportion of auto
accidents that involve teenage drivers is greater than 10%. ABC
Insurance Company checks police records on 200 randomly selected
auto accidents and notes that teenagers were at the wheel in 25 of
them.
Assume the company wants to use a 0.10 significance
level to test the researcher’s claim.
(a) What is the appropriate hypothesis test to use
for this analysis: onesample ztest for the population proportion,
onesample ttest for population proportion, onesample ztest for
population mean, or onesample t test for population mean? Please
identify and explain why it is appropriate.
(b) Identify the null hypothesis and the alternative
hypothesis.
(c) Determine the test statistic. Round your answer
to two decimal places.
Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
(d) Determine the
Pvalue for this test. Round your answer to three decimal
places.
Show all work; writing the correct Pvalue, without supporting
work, will receive no credit.
(e) Compare pvalue and significance level α. What
decision should be made regarding the null hypothesis (e.g., reject
or fail to reject) and why?
(f) Is there sufficient evidence to support the
researcher’s claim that the proportion of auto accidents that
involve teenage drivers is greater than 10%? Explain
17.Mimi was curious if regular excise really helps
weight loss, hence she decided to perform a hypothesis test. A
random sample of 5 UMUC students was chosen. The students took a
30minute exercise every day for 6 months. The weight was recorded
for each individual before and after the exercise regimen. Does the
data below suggest that the regular exercise helps weight loss?
Assume Mimi wants to use a 0.05 significance level to test the
claim
(a) What is the appropriate hypothesis test to use
for this analysis: ztest for two proportions, ttest for two
proportions, ttest for two dependent samples (matched pairs), or
ttest for two independent samples? Please identify and explain why
it is appropriate.
(b) Let μ
1 = mean weight before the exercise regime. Let μ
2 = mean weight after the exercise regime. Which
of the following statements correctly defines the null hypothesis?
(i) μ
1  μ
2 > 0 (μ
d > 0)
(ii) μ
1  μ
2 = 0 (μ
d = 0)
(iii) μ
1  μ
2 < 0 (μ
d < 0)
(c) Let μ
1 = mean weight before the exercise regime. Let μ
2 = mean weight after the exercise regime. Which
of the following statements correctly defines the alternative
hypothesis?
(a) μ
1  μ
2 > 0 (μ
d > 0)
(b) μ
1  μ
2 = 0 (μ
d = 0)
(c) μ
1  μ
2 < 0 (μ
d < 0)
(d) Determine the test statistic. Round your answer
to three decimal places.
Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
(e) Determine the pvalue. Round your answer to three
decimal places.
Show all work; writing the correct critical value, without
supporting work, will receive no credit.
(f) Compare pvalue and significance level α. What
decision should be made regarding the null hypothesis (e.g., reject
or fail to reject) and why?
(g) Is there sufficient evidence to support the claim
that regular exercise helps weight loss? Justify your conclusion.
18.The UMUC Daily News reported that the color
distribution for plain M&M’s was: 40% brown, 20% yellow, 20%
orange, 10% green, and 10% tan
.Each piece of candy in a random sample of 100
plain M&M’s was classified according to color
,and the results are listed below. Use a 0.05
significance level to test the claim that the published color
distribution is correct.
Show all work and justify your answer.Color

Brown

Yellow

Orange

Green

Tan

Number

42

18

15

7

18
(a) What is the appropriate hypothesis test: ztest
for sample proportion, ttest for sample mean, chisquare goodness
of fit test, Ftest for ANOVA? Please identify and explain why it
is appropriate for analyzing this data.
(b) Identify the null hypothesis and the alternative
hypothesis.
(c) Determine the test statistic. Round your answer
to two decimal places.
Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
(d) Determine the Pvalue. Round your answer to two
decimal places.
Show all work; writing the correct Pvalue, without supporting
work, will receive no credit.
(e) Compare pvalue and significance level α. What
decision should be made regarding the null hypothesis (e.g., reject
or fail to reject) and why?
(f) Is there sufficient evidence to support the claim
that the published color distribution is correct? Justify your
answer
19. A STAT 200 instructor believes that the
average quiz score is a good predictor of final exam score. A
random sample of 10 students produced the following data where
xis the average quiz score and
yis the final exam score.
x

80

95

50

60

100

55

85

70

75

85

y

70

96

50

63

96

60

83

60

77

87
(a) Find an equation of the least squares regression
line. Round the slope and yintercept value to two decimal places.
Describe method for obtaining results. Show all work; writing
the correct equation, without supporting work, will receive no
credit.
(b) Based on the equation from part (a), what is the
predicted final exam score if the average quiz score is 65?
Show all work and justify your answer.
(c) Based on the equation from part (a), what is the
predicted final exam score if the average quiz score is 40? Show
all work and justify your answer.
(d) Which predicted final exam score that you
calculated for (b) and (c) do you think is closer to the true final
exam score and why
20.What is the appropriate statistical analysis to
use: ttest for two independent samples, ttest for dependent
samples, ANOVA, or chisquare test of independence? Please identify
and explain why it is appropriate
(a) A study was conducted to see whether monetary
incentives to use less water during times of drought had an effect
on water usage. Sixty single family homeowners were randomly
assigned to one of two groups: 1) monetary incentives and 2) no
monetary incentives. At the end of three months, the total amount
of water usage for each household, in gallons, was measured.
(b) A study was conducted to see whether the mean
weight loss is the same for 10 different weight loss programs. Each
of the 10 programs had 50 subjects in it. The subjects were
followed for 12 months. Weight change for each subject was recorded
1.The U.S. Census Bureau needs to estimate the
median income of females in the U.S. They collect incomes from 3500
females. Choose the best answer.
Justify for full credit.
1.
Justify for full credit
(a) Which of the followings is the variable?
(i) Female in the US
(ii) Income of a female in the US
(iii) Set of income responses from all females in the
US
(iv) Median income of set of all females in the US
(b) Which of the followings is the parameter?
(i) Female in the US
(ii) Income of a female in the US
(iii) Set of income responses from all females in the US
(iv) Median income of set of all females in the US
2.Choose the best answer.
Justify for full credit.
2.
Justify for full credit.
(a) The hotel ratings are usually on a scale from 0
star to 5 stars. The level of this measurement is
(i) interval
(ii) nominal
(iii) ordinal
(iv) ratio
(b) In a career readiness research, 100 students were
randomly selected from the psychology program, 150 students were
randomly selected from the communications program, and 120 students
were randomly selected from cyber security program. This type of
sampling is called:
(i) cluster
(ii) convenience
(iii) systematic
(iv) stratified
3. The midterm exam scores in a statistics class are shown
in the following table:
3. The midterm exam scores in a statistics class are shown
in the following table:
67

92

76

47

85

70

87

76

67

72

84

85

65

82

84

98

81

85

87

83

67

92

76

47

85

70

87

76

67

72

84

85

65

82

84

98

81

85

87

83

67

92

76

47

85

70

87

76

67

72

67
67

92
92

76
76

47
47

85
85

70
70

87
87

76
76

67
67

72
72

84

85

65

82

84

98

81

85

87

83

84
84

85
85

65
65

82
82

84
84

98
98

81
81

85
85

87
87

83
83
(a) Complete the following frequency distribution
table using 6 classes: 4049, 5059, 6069, 7079, 8089, and
9099. Express the cumulative relative frequency to two decimal
places. (
Show all work. Just the answer, without supporting work, will
receive no credit.)
Show all work. Just the answer, without supporting work, will
receive no credit.)
(b) What percentage of the midterm exam scores was at
least 70?
4.Answer the following questions based on the
midterm exam score data given in Question # 3
:
(Show all work. Just the answer, without supporting work, will
receive no credit.)
4.
:
(Show all work. Just the answer, without supporting work, will
receive no credit.)
(a) What is the range of the midterm exam scores
?
?
(b) What is the median of the midterm exam scores?
(c) What is the mode of the midterm exam scores
5.A STAT 200 professor took a sample of 10 midterm
exam scores from a class of 30 students. The 10 scores are shown in
the table below:
5.
95

67

76

47

85

70

87

80

67

72

95

67

76

47

85

70

87

80

67

72

95

67

76

47

85

70

87

80

67

72

95
95

67
67

76
76

47
47

85
85

70
70

87
87

80
80

67
67

72
72
(a) What is the sample mean?
(b) What is the sample standard deviation? (Round
your answer to two decimal places)
(c) If you leveraged technology to get the answers
for part (a) and/or part (b), what technology did you use? If an
online applet was used, please list the URL, and describe the
steps. If a calculator or Excel was used, please write out the
function
6.There are 4 suits (heart, diamond, clover, and
spade) in a 52card deck, and each suit has 13 cards. Suppose your
experiment is to draw one card from a deck and observe what suit it
is.
6.
Express the probability in fraction format. (
Show all work. Just the answer, without supporting work, will
receive no credit.)
Show all work. Just the answer, without supporting work, will
receive no credit.)
(a) Find the probability of drawing a heart or
diamond.
(b) Find the probability that the card is not a spade
7.There are 2 white balls and 8 red balls in an
urn. Consider selecting one ball at a time from the urn. What is
the probability that the first ball is red and the second ball is
also red? Express the probability in fraction format. (
Show all work. Just the answer, without supporting work, will
receive no credit.)
7.
Show all work. Just the answer, without supporting work, will
receive no credit.)
(a) Assuming the ball selection is with replacement.
(b) Assuming the ball selection is without
replacement
8.
There are twenty stores for a grocery chain in the
MidAtlantic region. The regional executive wants to visit five of
the twenty stores. She asks her assistant to choose five stores and
arrange the visit schedule. (
Show all work. Just the answer, without supporting work, will
receive no credit).
8.
8.
Show all work. Just the answer, without supporting work, will
receive no credit).
(a) Does the order matter in the scheduling?
(b) Based on your answer to part (a), should you use
permutation or combination to find the different schedules that the
assistant may arrange?
(c) How many different schedules can the assistant
recommend
9.Mimi has seven books from the Statistics is Fun
series. She plans on bringing two of the seven books with her in a
road trip. (
Show all work. Just the answer, without supporting work, will
receive no credit).
9.
Show all work. Just the answer, without supporting work, will
receive no credit
(a) Does the order matter in the book selection?
(b) Based on your answer to part (a), should you use
permutation or combination to find the number of the different ways
the two books can be selected?
(c) How many different ways can the two books be
selected
10. Let random variable
xrepresent the number of heads when a fair coin is tossed
two times.
10
x
(a) Construct a table describing the probability
distribution.
x

P(x)

0

1

2

x

P(x)

0

1

2

x

P(x)

x
x

P(x)
P(x)

0

0
0

1

1
1

2

2
2
(b) Determine the mean and standard deviation of
x.
Show all work. Just the answer, without supporting work, will
receive no credit
x
Show all work. Just the answer, without supporting work, will
receive no credit
11.Mimi plans make a random guess at 10
trueorfalse questions. Answer the following questions:
11.
(a) Let X be the number of correct answers Mimi gets.
As we know, the distribution of X is a binomial probability
distribution. What is the number of trials (n), probability of
successes (p) and probability of failures (q), respectively?
(b) Find the probability that she gets at most 5
correct answers. (Round the answer to 3 decimal places.
(c) To get the answers for part (b), what technology
did you use? If an online applet was used, list the URL and
describe the steps. If a calculator or Excel was used, write out
the function
12.The heights of pecan trees are normally
distributed with a mean of 10 feet and a standard deviation of 2
feet.
Show all work. Just the answer, without supporting work, will
receive no credit.
12.
Show all work. Just the answer, without supporting work, will
receive no credit.
(a) What is the probability that a randomly selected
pecan tree is between 9 and 12 feet tall? (round the answer to 4
decimal places)
(b) Find the 75
th percentile of the pecan tree height
distribution. (round the answer to 2 decimal places)
th
(c) To get the answers for part (a) and part (b),
what technology did you use? If an online applet was used, list the
URL and describe the steps. If a calculator or Excel was used,
write out the function
13.Based on the performance of all individuals who
tested between July 1, 2014 and June 30, 2017, the GRE Verbal
Reasoning scores are normally distributed with a mean of 150.05 and
a standard deviation of 8.43. (
https://www.ets.org/s/gre/pdf/gre_guide_table1a.pdf).
Show all work. Just the answer, without supporting work, will
receive no credit.
13.
https://www.ets.org/s/gre/pdf/gre_guide_table1a.pdf
Show all work. Just the answer, without supporting work, will
receive no credit.
(a) Consider all random samples of 36 test scores.
What is the standard deviation of the sample means? (Round your
answer to three decimal places)
(b) What is the probability that 36 randomly selected
test scores will have a mean test score that is between 150 and
155? (Round your answer to four decimal places)
(c) To get the answer for part (b), what technology
did you use? If an online applet was used, list the URL and
describe the steps. If a calculator or Excel was used, write out
the function
14.A survey showed that 1200 of the 1600 adult
respondents believe in global warming.
14.
(a) Construct a 95% confidence interval estimate of
the proportion of adults believing in global warming.
Show all work. Just the answer, without supporting work, will
receive no credit. Include description of how confidence interval
was constructed.
Show all work. Just the answer, without supporting work, will
receive no credit. Include description of how confidence interval
was constructed.
(b) Describe the confidence interval in everyday
language
15.A city built a new parking garage in a business
district. For a random sample of 100 days, daily fees collected
averaged $2,000, with a standard deviation of $500.
15.
(a) Construct a 90% confidence interval estimate of
the mean daily income this parking garage generates.
Show all work. Just the answer, without supporting work, will
receive no credit. Include description of how confidence interval
was constructed.
Show all work. Just the answer, without supporting work, will
receive no credit. Include description of how confidence interval
was constructed.
(b) Describe the confidence interval in everyday
language
16.A researcher claims the proportion of auto
accidents that involve teenage drivers is greater than 10%. ABC
Insurance Company checks police records on 200 randomly selected
auto accidents and notes that teenagers were at the wheel in 25 of
them.
16.
Assume the company wants to use a 0.10 significance
level to test the researcher’s claim.
(a) What is the appropriate hypothesis test to use
for this analysis: onesample ztest for the population proportion,
onesample ttest for population proportion, onesample ztest for
population mean, or onesample t test for population mean? Please
identify and explain why it is appropriate.
(b) Identify the null hypothesis and the alternative
hypothesis.
(c) Determine the test statistic. Round your answer
to two decimal places.
Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
(d) Determine the
Pvalue for this test. Round your answer to three decimal
places.
Show all work; writing the correct Pvalue, without supporting
work, will receive no credit.
P
Show all work; writing the correct Pvalue, without supporting
work, will receive no credit.
(e) Compare pvalue and significance level α. What
decision should be made regarding the null hypothesis (e.g., reject
or fail to reject) and why?
(f) Is there sufficient evidence to support the
researcher’s claim that the proportion of auto accidents that
involve teenage drivers is greater than 10%? Explain
17.Mimi was curious if regular excise really helps
weight loss, hence she decided to perform a hypothesis test. A
random sample of 5 UMUC students was chosen. The students took a
30minute exercise every day for 6 months. The weight was recorded
for each individual before and after the exercise regimen. Does the
data below suggest that the regular exercise helps weight loss?
Assume Mimi wants to use a 0.05 significance level to test the
claim
17.
(a) What is the appropriate hypothesis test to use
for this analysis: ztest for two proportions, ttest for two
proportions, ttest for two dependent samples (matched pairs), or
ttest for two independent samples? Please identify and explain why
it is appropriate.
(b) Let μ
1 = mean weight before the exercise regime. Let μ
2 = mean weight after the exercise regime. Which
of the following statements correctly defines the null hypothesis?
1
2
(i) μ
1  μ
2 > 0 (μ
d > 0)
1
2
d
(ii) μ
1  μ
2 = 0 (μ
d = 0)
1
2
d
(iii) μ
1  μ
2 < 0 (μ
d < 0)
1
2
d
(c) Let μ
1 = mean weight before the exercise regime. Let μ
2 = mean weight after the exercise regime. Which
of the following statements correctly defines the alternative
hypothesis?
1
2
(a) μ
1  μ
2 > 0 (μ
d > 0)
1
2
d
(b) μ
1  μ
2 = 0 (μ
d = 0)
1
2
d
(c) μ
1  μ
2 < 0 (μ
d < 0)
1
2
d
(d) Determine the test statistic. Round your answer
to three decimal places.
Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
(e) Determine the pvalue. Round your answer to three
decimal places.
Show all work; writing the correct critical value, without
supporting work, will receive no credit.
Show all work; writing the correct critical value, without
supporting work, will receive no credit.
(f) Compare pvalue and significance level α. What
decision should be made regarding the null hypothesis (e.g., reject
or fail to reject) and why?
(g) Is there sufficient evidence to support the claim
that regular exercise helps weight loss? Justify your conclusion.
18.The UMUC Daily News reported that the color
distribution for plain M&M’s was: 40% brown, 20% yellow, 20%
orange, 10% green, and 10% tan
.Each piece of candy in a random sample of 100
plain M&M’s was classified according to color
,and the results are listed below. Use a 0.05
significance level to test the claim that the published color
distribution is correct.
Show all work and justify your answer.Color

Brown

Yellow

Orange

Green

Tan

Number

42

18

15

7

18

18.The UMUC Daily News reported that the color
distribution for plain M&M’s was: 40% brown, 20% yellow, 20%
orange, 10% green, and 10% tan
.Each piece of candy in a random sample of 100
plain M&M’s was classified according to color
,and the results are listed below. Use a 0.05
significance level to test the claim that the published color
distribution is correct.
Show all work and justify your answer.Color

Brown

Yellow

Orange

Green

Tan

Number

42

18

15

7

18

18.The UMUC Daily News reported that the color
distribution for plain M&M’s was: 40% brown, 20% yellow, 20%
orange, 10% green, and 10% tan
.Each piece of candy in a random sample of 100
plain M&M’s was classified according to color
,and the results are listed below. Use a 0.05
significance level to test the claim that the published color
distribution is correct.
Show all work and justify your answer.Color

Brown

Yellow

Orange

Green

Tan

18.The UMUC Daily News reported that the color
distribution for plain M&M’s was: 40% brown, 20% yellow, 20%
orange, 10% green, and 10% tan
.Each piece of candy in a random sample of 100
plain M&M’s was classified according to color
,and the results are listed below. Use a 0.05
significance level to test the claim that the published color
distribution is correct.
Show all work and justify your answer.Color
18.The UMUC Daily News reported that the color
distribution for plain M&M’s was: 40% brown, 20% yellow, 20%
orange, 10% green, and 10% tan
.Each piece of candy in a random sample of 100
plain M&M’s was classified according to color
,and the results are listed below. Use a 0.05
significance level to test the claim that the published color
distribution is correct.
Show all work and justify your answer.Color
18.
.
,
Show all work and justify your answer.

Brown
Brown

Yellow
Yellow

Orange
Orange

Green
Green

Tan
Tan

Number

42

18

15

7

18

Number
Number

42
42

18
18

15
15

7
7

18
18
(a) What is the appropriate hypothesis test: ztest
for sample proportion, ttest for sample mean, chisquare goodness
of fit test, Ftest for ANOVA? Please identify and explain why it
is appropriate for analyzing this data.
(b) Identify the null hypothesis and the alternative
hypothesis.
(c) Determine the test statistic. Round your answer
to two decimal places.
Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
(d) Determine the Pvalue. Round your answer to two
decimal places.
Show all work; writing the correct Pvalue, without supporting
work, will receive no credit.
Show all work; writing the correct Pvalue, without supporting
work, will receive no credit.
(e) Compare pvalue and significance level α. What
decision should be made regarding the null hypothesis (e.g., reject
or fail to reject) and why?
(f) Is there sufficient evidence to support the claim
that the published color distribution is correct? Justify your
answer
19. A STAT 200 instructor believes that the
average quiz score is a good predictor of final exam score. A
random sample of 10 students produced the following data where
xis the average quiz score and
yis the final exam score.
x

80

95

50

60

100

55

85

70

75

85

y

70

96

50

63

96

60

83

60

77

87

19. A STAT 200 instructor believes that the
average quiz score is a good predictor of final exam score. A
random sample of 10 students produced the following data where
xis the average quiz score and
yis the final exam score.
x

80

95

50

60

100

55

85

70

75

85

y

70

96

50

63

96

60

83

60

77

87

19. A STAT 200 instructor believes that the
average quiz score is a good predictor of final exam score. A
random sample of 10 students produced the following data where
xis the average quiz score and
yis the final exam score.
x

80

95

50

60

100

55

85

70

75

85

19. A STAT 200 instructor believes that the
average quiz score is a good predictor of final exam score. A
random sample of 10 students produced the following data where
xis the average quiz score and
yis the final exam score.
x
19. A STAT 200 instructor believes that the
average quiz score is a good predictor of final exam score. A
random sample of 10 students produced the following data where
xis the average quiz score and
yis the final exam score.
x
19
x
y
x
x

80
80

95
95

50
50

60
60

100
100

55
55

85
85

70
70

75
75

85
85

y

70

96

50

63

96

60

83

60

77

87

y
y
y
y

70
70

96
96

50
50

63
63

96
96

60
60

83
83

60
60

77
77

87
87
(a) Find an equation of the least squares regression
line. Round the slope and yintercept value to two decimal places.
Describe method for obtaining results. Show all work; writing
the correct equation, without supporting work, will receive no
credit.
Describe method for obtaining results. Show all work; writing
the correct equation, without supporting work, will receive no
credit.
(b) Based on the equation from part (a), what is the
predicted final exam score if the average quiz score is 65?
Show all work and justify your answer.
Show all work and justify your answer.
(c) Based on the equation from part (a), what is the
predicted final exam score if the average quiz score is 40? Show
all work and justify your answer.
(d) Which predicted final exam score that you
calculated for (b) and (c) do you think is closer to the true final
exam score and why
20.What is the appropriate statistical analysis to
use: ttest for two independent samples, ttest for dependent
samples, ANOVA, or chisquare test of independence? Please identify
and explain why it is appropriate
20.
(a) A study was conducted to see whether monetary
incentives to use less water during times of drought had an effect
on water usage. Sixty single family homeowners were randomly
assigned to one of two groups: 1) monetary incentives and 2) no
monetary incentives. At the end of three months, the total amount
of water usage for each household, in gallons, was measured.
(b) A study was conducted to see whether the mean
weight loss is the same for 10 different weight loss programs. Each
of the 10 programs had 50 subjects in it. The subjects were
followed for 12 months. Weight change for each subject was recorded

















