A study published in 2009 (Goldstein et al, 2009) asked a random selection of 499 adults from various regions in Israel to do a survey about whether or not they read while using the toilet. The researchers conducted a test of 2: = 0.5 versus 5: 0.5 where is the proportion of adults who read while using the toilet.

a) Use a theory-based method to find the rejection region of the test using a significance level of = 0.1 and as the test statistic. Recall, the rejection region is the set of values of that would lead the researchers to reject the null hypothesis.

b) Suppose the true proportion of adults who read while sitting on the toilet is 50%. What is the probability the researchers will incorrectly conclude that the proportion is different from 50%?

c) Suppose the true proportion of adults who read while sitting on the toilet is 55%. Use a theory-based method to calculate the probability the test will reveal that the alternative hypothesis is true.

d) Suppose the researchers were able to collect more data from another 100 adults, so they had a total of 599 adults in their sample. What would happen to the power of the test; would it increase, decrease, or stay the same? Explain.