Hypothesis tests. 4 questions in total, I have already done one but am unsure of how to do the others. Should only take over an hour to finish.

Worcester State University MA150 Statistics

Chapter 9 Writeup Instructor: Mary Fowler

Name: Dylan Smith Section: OL3

1. The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.4 parts per million (ppm). A consumer health group measured the level of the chemical in a random sample of tomatoes obtained from one producer. The levels, in ppm, are shown below.

0.31 0.47 0.19 0.72 0.56

0.91 0.29 0.83 0.49 0.28

0.31 0.46 0.25 0.34 0.17

0.58 0.19 0.26 0.47 0.81

At the 5% significance level, do the data provide sufficient evidence to conclude that the mean level of the chemical in tomatoes from this producer is greater than the recommended level of 0.4 ppm? Assume that the population standard deviation of levels of the chemical in these tomatoes is 0.21 ppm and that the distribution of ppm is normally distributed. Use the critical value approach.

X= .4445 s = .21 n = 20 H0 = .4 H1 > .4

ta = .05 = 1.729

.4445 + .0812 = (.3633, 5357) t = .4445 - .4 = .9477

.21 /

The data cannot be rejected since it provides evidence that the ppm can rise above .4 ppm.

1. In 2000, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 2000 mean of 9.4 minutes. They randomly sampled 50 calls originating in the town and found that the mean duration of these 50 calls was 8.6 minutes. Do the data provide sufficient evidence to conclude that the mean call duration has changed from the 2000 mean of 9.4 minutes Perform the appropriate hypothesis test using a significance level of 0.01. Assume that the population standard deviation is 4.8 minutes. Use the p-value approach.

1. A large software company gives job applicants a test of programming ability and the mean for that test has been 160 in the past. Twenty-five job applicants are randomly selected from a large university and they produce a mean score of 183 and standard deviation of 12. Assume the distribution of test scores is normally distributed. Use a 0.05 level of significance to test whether the mean score for students from this university is greater than 160.

1. Historically, a local police department has issued 60 speeding tickets a day in their area. After installing new speed limit signs they think the number of speeding tickets might have decreased. To test this, they randomly select two weeks and record the number of tickets issued for each day. The data are listed below. Assume the distribution of number of speeding tickets is normally distributed. At α = 0.01, test the claim that the number of speeding tickets in the area has decreased.