Hypothesis Tests

If you live in California, the decision to buy earthquake insurance is an important one. A survey revealed that only 133 of 337 randomly selected residences in one California county were protected by earthquake insurance. Calculate the appropriate test statistic to test the hypotheses that at least 40% buy the insurance. (rounded)

The average waiting time per customer at a fast food restaurant has been 7.5 minutes. The customer waiting time has a normal distribution. The manager claims that the use of a new cashier system will decrease the average customer waiting time in the store. Based on a random sample of 16 customer transactions the mean waiting time is 6.3 minutes and the standard deviation is 2 minutes per customer. Test the manager's claim at 5% and 1% significance level tests.

In an early study, researchers at an Ivy University found that 33% of the freshmen had received at least one A in their first semester. Administrators are concerned that grade inflation has caused this percentage to increase. In a more recent study, of a random sample of 500 freshmen, 185 had at least one A in their first semester Calculate the appropriate test statistic to test the hypotheses related to the concern and test at 5% and 1%.

A microwave manufacturing company has just switched to a new automated production system. Unfortunately, the new machinery has been frequently failing and requiring repairs and service. The company has been able to provide its customers with a completion time of 6 days or less. To analyze whether the completion time has increased, the production manager took a sample of 36 jobs and found that the sample mean completion time was 6.5 days with a sample standard deviation of 1.5 days. At significance levels of .05 and .10, test whether the completion time has increased. Indicate which test you are performing; show the hypotheses, the test statistic and the critical values and mention whether one-tailed or two-tailed.

State True or False: First a confidence interval is constructed without using the finite population correction factor. Then, for the same identical data, a confidence interval is constructed using the finite population correction factor. The width of the interval with the finite population correction factor is wider than the confidence interval without the finite population correction factor.

State True or False: When the population is normally distributed and the population standard deviation is unknown, then for any sample size, the sampling distribution is based on the t distribution.