An experiment compared the taste of two types of coffee, a store brand and a brand of coffee called Freshly Brewed. Each randomly selected participant tastes two unmarked cups of coffee in random order and states which he or she prefers. Of the 50 people sampled, 34 preferred Freshly Breved coffee. Let p denote the true proportion of all people who prefer Freshly Brewed coffee.
a) Do people prefer Freshly Brewed than the store brand? Suppose you'd like to conduct a hypothesis test to answer this question. State your Ho and Ha Check the assumptions and conditions required to do the hypothesis test.
b) Given the sample size, what is the smallest value of p that would lead you to reject Ho? Use a significance level of 0.1.
c) State your conclusions for the hypothesis test based on your results in (b).
d) Use the critical value approach method now.
e) Calculate an appropriate confidence interval (two sided or one sided) and explain how it can be used to test the hypotheses.
f) Calculate the power of the test, if the true proportion is 0.6.
g) How can we increase the power of the test -state all possible methods.
h) Freshly Brewed would like to sponsor your experiment. Would Freshly Brewed be more concerned about Type I error or Type II error? Explain.