8.17. The mean work week for engineers in a start-up company is believed to be about 60 hours, on average. A newly hired engineer hopes that it's shorter. She asks ten engineering triends in start-ups for the lengths of their mean work weeks. The sample average was 58.1 hours and the standard deviation was 3.4 hours. Should she count on the mean work week to be shorter than 60 hours? Conduct a hypothesis test at the 5% significance level. Show all steps of the test. 8.22. A study is done to determine if company A retains workers longer than company B. In a sample of 15 workers at company A, the average time they stay with the company is 4 years with standard deviation ct 1.2 years. In a sample 0120 workers at company B, the average time they stay with the company is 3.5 years with standard deviation at 1 years. Pertorm all the steps of a hypothesis test at the 10% level of significance to determine if company A retains workers longer than company B, on average. 8.28. Ten years ago, it was found that only 28% of manufacturing companies believed that their operations had a negative environmental effect. In a more recent survey, 127 out of 250 companies indicated that they believe their operations have a negative effect on the environment. Conduct a hypothesis test at the 5% level of significance to determine if there is evidence that the proportion increased from the previous 28%. 8.33. An airline company is wondering how many of its customers are children. Specifically, the company is wondering if more than 5% of its customers are children. The hypotheses are then Ho : p g 0.05 and H1 : p > 0.05. Suppose that the null hypothesis was not rejected and it was determined that p = 0.06. What type of error, if any, occurred? 8.34. A manager at a company claims that the new advertising project proposed will increase the annual sales by 6%. The hypotheses are H0 : ,u = 6 vs. H1 : ,u 7% 6. Using sample data of the first month, he conducted a test of significance and rejected the null hypothesis. At the end of the year, it is tound that the total sales has increased by 6.4%. What type 01 error, if any, occurred