A restaurant chain with multiple branches would like to measure the effectiveness of a customer skills training program for its employees. A random sample of 30 branches is chosen, and the daily sales for these branches are recorded. All the employees at these branches then undergo a customer skills training program, and shortly thereafter the daily sales at these 30 branches are again recorded. (a) Which type of test should the company use to determine if the customer skills program helped increase sales? a. One sample t-test b. Paired t-test c. Chi-squared test of independence d. One proportion z-test OTwo sample t-test (independent means) (b) A Type II error in this context means the company finds evidence of an increase in sales, when in reality there is in sales.

A) Option B: Paired t-test

B) The company finds "SUFFICIENT" evidence of an increase in sales, when in reality there is "A DECREASE" in sales

Step-by-step explanation:

A) Let's look at the options.

a) One sample t-test: This t-test is a statistical hypothesis test that's used to find out whether an unknown population mean has a different value from the sample mean.

b) Paired t-test: This is used to compare mean at different times from the same group.

c) Chi-squared test of independence: This test is one that is used to determine whether the associated variables are related or independent.

d) One proportion z-test: This test is used to compare an observed proportion to that of a theoretical proportion.

e) Two sample t-test: This is used to test if the unknown population mean that is gotten from two groups are equal or not.

Now, from the question, we see that A random sample of 30 branches is chosen, and the daily sales for these branches are recorded.

Later on, All the employees at these branches then undergo a customer skills training program, and shortly thereafter the daily sales at these 30 branches are again recorded.

This means that we are trying to compare the mean within the same group but at different times. This corresponds to the definition of Paired t-test.

B) A Type II error occurs when we accept a null hypothesis that is actually false.

The type II error in this case is that:

The company finds "SUFFICIENT" evidence of an increase in sales, when in reality there is "A DECREASE" in sales