Chapter 9.6, Problem 66PB

Exploring Type II errors Refer to the web app from Activity 2 at the end of this section, now assuming that we are using the two-sided test H₀: p = 0.33 against H_a: p ≠ 0.33. (Select “not equal” for the type of the alternative hypothesis in the web app.)

1. a. Explain the effect of increasing the sample size on the probability of a Type II error when the true p = 0.50.
2. b. Use the app to find the sample size needed to achieve a power of at least 90% when truly p = 0.50.
3. c. For a fixed sample size, do you think the probability of a Type II error will increase or decrease when the true p is 0.40 instead of 0.50? Check your answer with the app.
4. d. Does the power increase or decrease when the significance level is 0.10 instead of 0.05? Check your answer with the app.