Suppose we are planning to conduct a randomized dietary intervention trial to prevent reoccurrence of breast cancer. Based on previous pilot studies, we anticipate the dietary intervention will reduce the breast cancer rate in the intervention group.

State the null and alternative hypotheses for this study

a. State the null and alternative hypotheses

b. Is the alternative hypothesis one-sided or two-sided? Why is your choice reasonable?

c. What is the Type 1 and Type 2 error of the conclusion of this study? State your answer in words.

**Solution: **(a) We have the following hypotheses

_{}

(b) The alternative hypothesis is one-sided. We see this by noticing that if we _{}to the current breast cancer rate, the null hypothesis states that_{}, and the alternative hypothesis state that_{}, where_{}is the breast cancer rate *after* the dietary intervention.

(c) The type I error corresponds to the probability of rejecting that the dietary intervention won’t reduce the breast cancer rate when it actually didn’t reduce the rate and, type II error corresponds to the probability of accepting that the dietary intervention won’t reduce the breast cancer rate when it actually did reduce the rate.

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