1. For each the following variables from the Salary Data Set provide the measures of location and measures of dispersion for the following variables:
1. Beginning Salary
2. Previous Experience
3. Which variable has the greatest relative variability?
2. You are the manager of a high-end ladies fashion store. For the past few months you have been gathering data and found that 55% of persons entering the store actually make a purchase. Assume these data follow a Binomial Distribution and use Excel to calculate the following binomial probabilities:
1. If 15 people enter the store, what is the probability that exactly 8 of them will make a purchase?
2. What is the probability that more than 8 of the 15 people will make a purchase?
3. Using the Salary Data Set what is the probability of randomly selecting one individual (male or female) with a current annual salary of over $40,000?
4. The time required to complete a project is normally distributed with a mean of 77 weeks and a standard deviation of 4 weeks. The construction company must pay a penalty if the project is not finished by the due date of the contract. If a construction company bidding on this contract wishes to be 95 percent sure of finishing by the due date, use the NORMINV Excel Function to determine what due date (project week #) should be negotiated?
5. In a state lottery participants select 8 numbers between 1 and 49. At the end of the week, the state lottery commission randomly draws 8 numbers between 1 and 49. How many different possible winning number combinations could be drawn by the lottery commission?
6. From the Salary Data Set and assuming that the salary data is a random sample from the population of salaries from the multi-national company use the 95% confidence level in PHStat to estimate the mean beginning salary for company executives.
1. If you were to change the confidence level to 99%, what would happen to the confidence interval? What is the 99% confidence interval?
7. Using the Salary Data Set,
1. Create a scatter plot to show this relationship between education and current salary
2. Determine the correlation coefficient between the variables. What does this tell us about the relationship?
8. Explain why rejecting the null hypothesis does not make the alternative hypothesis true.
9. What is the purpose of statistical inference?
10. What is the difference between sampling error and the standard error of the mean?
11. You are a consultant working for Kaplan Consulting. The Director of Human Resources for a multi-national company has requested help in investigating a pay discrimination complaint brought by a female executive. The company provided the data in the Salary Data Set. Use PHStat and the appropriate t test, to investigate the claim of pay discrimination in the Beginning Salary.
“Is there a significant difference between the average female and average male salaries?”
1. What is the Null and the Alternative Hypotheses?
2. What is your level of alpha (α)?
Why did you choose this level? Please explain in terms of Type I or Type II errors.
3. What is the output from your analysis?
4. What is your decision about the hypothesis based on the software output?
5. Is there a significant difference between the average female and average male salaries? Please write a written statement to the director of Human Resources as to whether they should be concerned about the complaint.