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Show all your work. Indicate clearly the methods you use, because you will be scored on...

Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

A bank categorizes its customers into one of three groups based on their banking habits. A random sample of 30 customers from each group was selected, and the number of times each customer visited the bank during the past year was recorded. The following table shows the summary statistics.

Groups n x-bar s
A 30 48 7
B 30 51 8
C 30 54 10

The bank manager will investigate whether there is a significant difference in mean numbers of bank visits for the groups. Multiple two-sample t-tests will be conducted, each at the significance level of α=0.05.

The significance level (α) of a single hypothesis test is the probability of making a Type I error. The manager wants to know the probability of making a Type I error for multiple t-tests, not just for a single t-test. This probability is called the family error rate for Type I error, which is also known as the family error rate.

Question 4

(d) The manager wants the family error rate to be close to 0.05. Suggest a single significance level α that could be used for all of the individual t-tests that will bring the family error rate close to 0.05. Show work to support your suggested level.

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