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.

0.310.470.190.720.56

0.910.290.830.490.28

0.310.460.250.340.17

0.580.190.260.470.81

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 isgreaterthan the recommended level of0.4ppm? 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.

2.In 2000,the average duration oftelephone calls originating in one town was9.4 minutes.Along distancetelephone company wants to perform a hypothesis test to determine whether the average duration oflong-distancephone calls has changed from the 2000 mean of9.4 minutes.They randomly sampled 50 callsoriginating in the town and found that the mean duration of these 50 calls was8.6 minutes. Do the data provide sufficient evidence to conclude that the mean call duration, , haschangedfrom the 2000 mean of9.4 minutes?Perform the appropriate hypothesis test using a significance level of 0.01. Assume that= 4.8 minutes.Use the p-value approach.

3.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 isgreaterthan 160.

4.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 =0.01, test the claim that the number of speeding tickets in the area hasdecreased.

70 48 41 68 69 55 70 57 60 83 32 60 72 58

Also, Calculate the sample mean and standard deviation