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Hypothesis Testing – Comparing Two Groups

 

1For each of the following research questions does the situation or research question involve independent samples or paired data?

 

a.Do liberal arts majors and science majors have different SAT verbal scores, on average?

 

 

b.Does a caffeine pill help Autistic patients score higher on a cognitive exam?

 

 

c.In heterosexual relationships, does the man or the woman average more time outside the house?

 

 

d. Do families with at least one unemployed adult average more time watching TV per week than families in which all adults are employed?

 

In the Datasets folderopen the GSS Dataset.   The data are from the 2006 General Social Survey, a federally funded national survey done every other year by the University of Chicago. The variable marital indicates whether the respondent is presently married or not. We’ll compare the meanage ( Age is the variable) for those who are married versus those who are not. 

 

a.In words, write a null hypothesis for this situation. We’re comparing two means (age for married people versus unmarried people).

 

 

 

b.Using statistical notation for means write null and alternative hypotheses for this problem.

 

c.Recall from the lecture notes that when doing a two-sample t-test one consideration is whether the two standard deviations (or variances) are equal.  To check, use software to find the standard deviation for Agefor the two categories of maritalstatus.  In Minitab Express, you can get these SD by clicking Statistics > Descriptive Statistics and selecting Age for Variables and marital for Group variable. 

 

i.                   What are the two standard deviations?

Std.dev for married:

Std.dev for not married:

 

 

            ii.Is the larger standard deviation more thantwice the smaller standard deviation?

 

 

            iii.If your answer to part iiis “Yes” then we will use the unpooledmethod for calculating the standard error.  If your answer was “No” then we can use the pooledmethod.  Which method should we use?

 

 

 

d.The two-sample t-test is used to compare means when data is from two independent samples (as it is here). Use software to conduct a 2-sample t test. If your answer to part iiiabove is “NO” use pooledthen click the box for “Assume Equal Variances”. Read the output to find the values of the t-statistic and the p-value.

 

      t=                                           p-value =

 

e. State a conclusion about the hypotheses and about the “real world” situation.

 

 

f. The formula for the pooled t-statistic is .  Give values for each of the elements in the formula. 

                                                                              

 

g.The output includes a 95% confidence interval for the difference between means. Write a sentence that interprets this interval in terms of how much difference there is between the mean ages of the two groups.

 

 

 

h.Refer again the to the 95% confidence interval of the previous part. Explain why it is evidence that makes it reasonable to conclude that the population means differ.

 

 

3In a national survey of 12 thgraders, 254 of 1356 boys said they never or rarely wear a seatbelt when driving. Among 1168 girls, 197 said they never or rarely wear a seatbelt when driving.

 

a.Let p 1= population proportion that never or rarely wears a seatbelt for boys and p 2= the corresponding proportion for girls. Write null and alternative hypotheses about p 1and p 2for testing if a difference exists.

 

 

b. If using Minitab Express, then use Statistics > Two Samples > Proportions.  Click on the drop-down menu under the word “Data” and select Summarized data. Use the boys as the first sample and girls as the second sample. “Number of trials” means sample size and “Number of events” means number rarely or never wearing a seatbelt. Next click Optionsand select your alternative hypothesis and enter your test difference.  If your hypotheses statements are testing that the difference is 0, then be sure to select the Use the pooled estimate of the proportionfor your test method Use the output to give values for the following:

 

For boys, sample proportion =    _______     For girls, sample proportion =  =  ________

 

The difference between the sample proportions is  =_______

 

Value of test statistic =  _________                                       p-value = _______

 

c.Explain whether we can we say there is a difference between the population proportions in this situation.

 

4  In the Datasets folderclick the link for the Class Survey.  Is there a difference in the number of parties attended each month and the number of days drinking alcohol?  Since we are considering differences between two measurements (i.e. Monthly Parties and Drinking Days) on the same individual we can consider the data to be paired.  Use software to conduct a Matched Pairs t-test

 

a.Write the null and alternative hypotheses using appropriate statistical notation.

 

H 0:                            H a:                   

 

b.Based on the Confidence interval what is your conclusion?

 

c.  Based on your p-value what is your conclusion?

 

d.Use the data from the output to calculate the t-statistic by:  t =

                                    

 

 

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