A study published in 2009 (Goldstein et al, 2009) askeda random selection of 499 adults from various regions in Israel tocomplete a survey about whether or not they read while using thetoilet. The researchers conducted a test of Ho: pi = 0.5 versus Ha:pi ≠0.5 where pi is the proportion of adults who read while usingthe toilet.
- Use a theory-based method to find the rejection region of thetest using a significance level of alpha = 0.1 and p-hat as thetest statistic. Recall, the rejection region is the set of valuesof p-hat that would lead the researchers to reject the nullhypothesis.
- Suppose the true proportion of adults who read while sitting onthe toilet is 50%. What is the probability the researchers willincorrectly conclude that the proportion is different from50%?
- Suppose the true proportion of adults who read while sitting onthe toilet is 55%. Use a theory-based method to calculate theprobability the test will reveal that the alternative hypothesis istrue.
- Suppose the researchers were able to collect more data fromanother 100 adults, so they had a total of 599 adults in theirsample. What would happen to the power of the test; would itincrease, decrease, or stay the same? Explain.
