Instructions: Complete each problem on a separate worksheet in a single Excel file. Rename the separate worksheets with the respective problem number. You may have to copy and paste the datasets into your homework file first. Name the file with your last name, first initial, and HW #7. Label each part of the question. When calculating statistics, label your outputs. Submit your completed file in Blackboard. If not significance level is specified, assume 5%.
1. The file 310homework7data.xlsx, problem #1 data contains a random sample of 100 lightbulb lifetimes. The company that produces these lightbulbs wants to know whether it can claim its lightbulbs typically last more than 1000 burning hours.
a. Identify the null and alternative hypotheses for this situation.
b. Can this lightbulb manufacturer claim that its lightbulbs typically last more than 1000 hours at the 5% significance level? What about at the 1% significance level? Explain.
2. A US Navy recruiting center knows from past experience that the heights of its recruits have traditionally been normally distributed with a mean of 69 inches. The recruiting center wants to test the claim that the average height of this year’s recruits is greater than 69 inches. A random sample of 64 recruits from this year is selected and their heights recorded. The data is in the file 310homework7data.xlsx in Problem #2.
a. Identify the null and alternative hypotheses for this situation.
b. On the basis of the available information, do the recruiters find support for the given claim at the 5% significance level? Explain.
c. Use the sample data to calculate a 95% confidence interval. What conclusion should the recruiting personnel reach regarding the given claim?
d. Are the results of c and d different? If so, explain why.
3. A study is performed in a large southern town to determine whether the average amount spent on food per four-person family in the town is significantly different from the national average. A random sample of the weekly grocery bills are given in the file 310homework7data.xlsx in Problem #3. Assume the national average amount spent on food in a 4-person family is $150.
a. Identify the null and alternative hypothesis for this situation.
b. For which values of the sample mean would you reject the null hypothesis at the 1% significance level? For which values of the sample mean would you reject the null hypothesis at the 10% significance level?
4. The CEO of a medical supply company is committed to expanding the proportion of highly qualified women in the organization’s staff of salespersons. He claims that the proportion of women in similar sales positions is across the country in 2016 is less than 50%. Hoping to find support for his claim, he directs his assistant to collect a random sample of salespeople employed by his company, which is thought to be representative of sales staffs of competing organizations in the industry. The data is given in the file 310homework7data.xlsx in Problem #4.
a. Is there statistical support for his hypothesis that the proportion of women in similar sales positions across the country is less than 50%? Why or why not? Be sure to clearly state the null and alternative hypotheses you are testing.
b. Compare the 2016 data to the 2011 data. If the 2011 data is representative, did the CEO’s push to hire more women work? Conduct an appropriate test and explain your reasoning. Be sure to state the null and alternative hypotheses.
5. A real estate agent has collected a random sample of 75 houses that were recently sold in a suburban community. She is particularly interested in comparing the appraised value and recent selling price of the houses in this particular market. The data is given in the file 310homework7data.xlsx in Problem #5. Using this sample data, test whether there is statistical difference between the appraised value and the selling price of the houses sold in this community. Report a p-value. For which levels of significance is it appropriate to conclude that no difference exists between these two values? Which is more appropriate: a one-tailed test, or two-tailed test? Explain.
6. Do undergraduate business students who major in finance earn, on average, higher annual starting salaries than their peers who major in marketing? Address this question through the data in the file 310homework7data.xlsx in Problem #6 which contains the starting salaries of 50 randomly selected finance majors and 50 randomly selected marketing majors.
a. Is it appropriate to perform a paired comparison test on this data? Why or why not?
b. Perform an appropriate hypothesis test with 5% significance level. Summarize your findings.
c. How large would the difference between the mean starting salaries of marketing and finance majors needs to be before you could conclude that the finance majors made more money?