Write your answers out clearly and neatly, and show all of your steps. Please use SAS to do this homework assignment. If applicable, explain why you chose a particular formula (e.g. why use an independent samples t-test instead of a paired t-test?). At the end of the homework assignment, append your SAS code (you may copy/paste your code after the last problem).
1. An industrial engineer conjectures that a major difference between successful and unsuccessful companies is the percentage of their manufactured products returned because of defectives. In a study to evaluate this conjecture, the engineer surveyed the quality control departments of 50 successful companies (identified by the annual profit statement) and 50 unsuccessful companies. the companies in the study all produced products of a similar nature and cost. The percentages of the total output returned by customers in the previous year are provided in the attached file.
a. Do the data provide sufficient evidence that successful businesses have a lower percentage of their products returned by customers? Use 𝛼 = 0.1.
b. What test did you use? What evidence do you have that the test’s assumptions are valid?
c. In order for the difference in percentage returns to have an economic impact, the difference must be at least 5%. Is there significant evidence that the percentage for successful businesses is at least 5% less than the percentage for unsuccessful businesses?
d. Estimate the difference in the percentages of returns for successful and unsuccessful businesses using a 95% confidence interval. Does this result agree with the hypothesis test in part a? Why or why not?
2. A study was designed to measure the effect of home environment on academic achievement of 12-year- old students. Because genetic differences may also contribute to academic achievement, the researcher wanted to control for this factor. Thirty sets of identical twins were identified who had been adopted prior to their first birthday, with one twin paced in a home in which academics were emphasized (Academic) and the other twin placed in a home in which academics were not emphasized (Nonacademic). The final grades (based on 100 points) for the 60 students are given in the attached file.
a. Is there a difference in the mean final grades between the students in an academically oriented home environment and those in a non-academically oriented home environment? Use 𝛼 = 0.05.
b. What test did you use? What evidence do you have that the test’s assumptions are valid?
c. Estimate the size of the difference in the mean final grades of the students in academic and nonacademic home environments using a 99% confidence interval.
d. Does it appear that using twins in this study to control for variation in final scores was effective as compared to taking a random sample of 30 students in both types of home environments? Why or why not?
3. A study was conducted to determine whether automobile repair charges are higher for female customers than for male customers. Twenty auto repair shops were randomly selected from the telephone book. Two cars of the same age, brand, and engine problem were used in the study. For each repair shop, the cars were randomly assigned to a male and a female participant and then taken to the shop for an estimate of repair cost. The repair cost (in dollars) is given in the attached file.
a. Are costs generally higher for female customers than male customers? Use 𝛼 = 0.1.
b. What test did you use? What evidence do you have that the test’s assumptions are valid?
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