For each of the following, state the null hypothesis and the alternative hypothesis:
a. The publisher of Celebrity Living claims that the mean sales of personality magazines featuring such celebrities as Angelina Jolie or Kim Kardashian is at least 1.5 million per week. A sample of 10 comparable titles shows that the mean weekly sales last week was 1.3 million. The publisher’s claim is to be verified.
b. The manager of Little Cakes Inc. states that an average of 1500 muffins is sold each week in the retail store. One of the bakers feels that the average is less than 1500 and decides to test this claim.
c. For the past three years, an insurance company has stated that its average claim amount is $2000. The manager feels that this amount should be updated and takes a sample of 55 claims to see if there is a difference in the average claim amount.
d. A machine on a production line is set to automatically fill each bottle with 500 mL of water. The quality control manager regularly takes random samples of the bottles from the production line to ensure that the machine is filling the bottles correctly. If not, the machine will need adjusting.