A telephone company claims that the mean duration of all long-distance phone calls made by its residential customers is 10 minutes. A random sample of 100 long-distance calls made by its residential customers taken from the records for this company showed that the mean duration of calls for this sample is 20 minutes. The population standard deviation is known to be 3.8 minutes. At the 0.02 level of significance, test the claim that the mean duration of calls made by residential customers is different from 10 minutes.
Dartmouth Distribution Warehouse makes deliveries of a large number of products to its customers. To keep its customers happy and satisfied, the company policy is to deliver on time at least 90% of the orders it receives from its customers. The quality control inspector at the company quite often takes samples of orders delivered and checks to see whether this policy is maintained. A recent sample of 90 orders taken by this inspector showed that 75 of them were delivered on time. Using the 2% level of significance, can you conclude that the company policy is maintained?
On a science assessment test, the scores of a random sample of 22 eighth-grade students have a standard deviation of 33.4 points. This result prompts the test administrator to claim that the standard deviation for eighth graders on the examination is less than 36 points. At α = 0.10, is there enough evidence to support the administrator's claim?