Part 2:Two Sample Testing using Calculator

You must show work to get full credit on these examples. You can type or hand answers.

Example 1: A company sells commercial bar glassware online notices that too much of their product is getting broken during shipping. They want to try out a new packing material to help fix this problem.

They randomly sample 250 shipments that use the old packing material and 250 shipments that are send in the new packing material. Using the old material 19 of the shipments reported product damage and using the new packing material only 13 of them reported damaged material. Assuming all conditions are met, test if the new packing material had smaller proportion of damaged product at = 0.05.

Set up the Hypotheses for this test:

Find the Test Statistic and p-value for this test:

Decision using the P-value Method (Show work):

Write a conclusion in context to the problem:

Example 2: Lei and Nasim own an interior design company with two location, one in Allegan and one in Kalamazoo. They think the store in Kalamazoo tends to bring in larger projects and are considering restructuring their business plan to accommodate.

Lei suggests before they make any big changes that they find out if the Kalamzoo store really does have a larger average project cost. They randomly samples 40 projects done at each location and got the following results. Test that the Kalamazoo location brings in projects with larger average cost at 5% significance level. Assume all conditions are met.

Location Allegan	Location Kalamazoo
Sample Mean: $2,720 Sample Standard Deviation: $820 Sample Size: 40	Sample Mean: $3,015 Sample Standard Deviation: $541 Sample Size: 40

Set up the Hypotheses for this test:

Find the Test Statistic for this test:

Decision using the Rejection Region Method (Show work):

Write a conclusion in context to the problem: