1. A manufacturer of television picture tubes has a production line that used to produce an average of 100 tubes per day. Because of new government a regulation, a new safety device is installed, which the manufacturer believes will reduce average daily output. After installation of the safety device, a random sample of 15 days' production was recorded, as follows:
93, 103, 98, 101, 93, 107, 96, 94, 101, 88, 98, 94, 101, 92, 96
Assuming that the daily output is normally distributed, is there sufficient evidence to allow the manufacturer to conclude that average daily output has decreased following installation of the safety device? (Use a significance level of 0.05).
a. State the null and alternative hypothesis that best tests the hypothesis of interest. Be sure to pay attention to whether this should be a 1-tailed or a 2-tailed test.
b. Carry out this test, and state whether you reject or fail to reject the null hypothesis. In computing the test statistic, be sure to indicate whether you are using "t" or "z". Use the precise critical value of the "t" or "z" you use, not an approximation.
c. Given your answer to part b., are you vulnerable to a Type I or Type II error? Explain why, in a single sentence.