Question

For each of the following, state the null hypothesis and the alternative hypothesis:

a. Means sales of Celebrity Living over the years have been 1.25 million per week. A manager claims that sales have increased.

H₀: μ           less-than or equal to, less-than, greater-than or equal to  1.25

H₁: μ greater-than, equal to, not equal to  1.25

b. The manager of Little Cakes Inc. states that an average of 1,500 muffins is sold each week in the retail store. One of the bakers feels that the average is greater than 1,500 and decides to test this claim.

H₀:           μless-than or equal to, less-than, greater-than or equal to  1,500.00

H₁:           μ not equal to, greater-than, equal to 1,500.00

c. For the past three years, an insurance company has stated that its average claim amount is $1,800. The manager feels that this amount should be updated and takes a sample of 65 claims to see if there is a difference in the average claim amount.

H₀:           μ equal to, less-than, greater-than or equal to  1,800

H₁:           μ   less-than or equal to, greater-than, not equal to  1,800

d. A machine on a production line is set to automatically fill each bottle with 400 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.

H₀:           μ   greater-than or equal to, equal to, less-than  400

H₁:           μgreater-than, less-than or equal to, not equal to  400

Answer 1

Solution-A:

sales have increased

Right tail

Ho:Mu<=1.25

Ha:Mu>1.25

H0: μ     less-than or equal to 1.25

H1: μ greater-than 1.25

Solution-B:

feels that the average is greater than 1,500

Ho:mu<=1500

Ha:mu>1500

H0:           μ less-than or equal to 1500

Ha:μ  greater-than 1500

Solution-c:

is a difference in the average claim amount.

its two tail test

H0:           μ equal to 1800

Ha:   μ not equal to 1800

Solution-d:L

if it fills correctly then mean to be 400

Ho:μ    equal to 400

Ha: μ not equal to  400