Chapter 10 hypothesis testing
The number of cars sold by three salespersons over a 6-month period are shown in the table below. Use the 5% level of significance to test for independence of salespersons and type of car sold
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- Insurance Preference
- QUESTIONS 84 AND 85 ARE BASED ON THE FOLLOWING INFORMATION
- Upper limit Category Frequency Normal
- Test of normal fit
- QUESTIONS 86 THROUGH 88 ARE BASED ON THE FOLLOWING INFORMATION
83. The number of cars sold by three salespersons over a 6-month period are shown in the table below. Use the 5% level of significance to test for independence of salespersons and type of car sold.
ANSWER:  We fail to reject the null hypothesis of independence at the 5% significance level (since p-value = 0.305 > 0.05). We may conclude that salespersons and type of car sold are independent. QUESTIONS 84 AND 85 ARE BASED ON THE FOLLOWING INFORMATION: An automobile manufacturer needs to buy aluminum sheets with an average thickness of 0.05 inch. The manufacturer collects a random sample of 40 sheets from a potential supplier. The thickness of each sheet in this sample is measured (in inches) and recorded. The information below are pertaining to the Chi-square goodness-of-fit test.
84. Are these measurements normally distributed? Summarize your results. ANSWER: Yes. Based on the Chi-square test, with a p-value of 0.545, you can conclude that the values are normally distributed. The frequency distribution also shows that the values are fairly close to the expected values. 85. Are there any weaknesses or concerns about your conclusions in Question 84? Explain your answer. ANSWER: Yes. There are a couple of concerns. The sample size is rather small (n = 40), you should use a larger sample size for this test to be more effective. Also, the test depends on which and how many categories are used for the histogram. A different choice could result in a different answer. QUESTIONS 86 THROUGH 88 ARE BASED ON THE FOLLOWING INFORMATION: Do undergraduate business students who major is computer information systems (CIS) earn, on average, higher annual starting salaries than their peers who major in international business (IB)?. To address this question through a statistical hypothesis test, the table shown below contains the starting salaries of 25 randomly selected CIS majors and 25 randomly selected IB majors.
86. Is it appropriate to perform a paired-comparison t-test in this case? Explain why or why not. ANSWER: A two-sample, not paired-sample, procedure should be used because there is no evidence of pairing. 87. Perform an appropriate hypothesis test with a 1% significance level. Assume that the population variances are equal. ANSWER:  ,  , Test statistic t = 6.22, P-value=0. Since P-value is virtually 0, we can conclude at the 1% level that the mean salary for CIS majors is indeed larger.
88. How large would the difference between the mean starting salaries of CIS and IB majors have to be before you could conclude that CIS majors earn more on average? Employ a 1% significance level in answering this question. ANSWER: P-value=0.01, t =2.41, and Standard error of difference =  . Then 
A mean difference of 1312.20 is all that would be required to get the conclusion in Question 87 at the 1% level. 89. A statistics professor has just given a final examination in his linear models course. He is particularly interested in determining whether the distribution of 50 exam scores is normally distributed. The data are shown in the table below. Perform the Lilliefors test. Report and interpret the results of the test. 77 71 78 83 84 71 81 82 79 71 73 89 74 75 93 74 88 83 90 82 79 62 73 88 76 76 76 80 84 84 91 70 76 74 68 80 87 92 84 79 80 91 74 69 88 84 83 87 82 72 ANSWER: The maximum distance between the empirical and normal cumulative distributions is 0.0802. This is less than 0.1247, the maximum allowed with a sample size of 50. Therefore, the normal hypothesis cannot be rejected at the 5% level. 
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