Problem 8.22 on page 504 of your text describes a matched pairs experiment, comparing the taste of instant versus fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 40 subjects who participate in the study, 12 prefer the instant coffee. Let p be the probability that a randomly chosen subject prefers fresh-brewed coffee to instant coffee. (In practical terms, p is the proportion of the population who prefer fresh-brewed coffee.)

(a) What is the purpose of presenting each subject two unmarked cups of coffee, one of each type, in random order?

(b) What is the Binomial distribution for the number of subjects (X) who prefer fresh-brewed coffee to instant coffee?

(c) To test the claim that majority of people prefer the taste of fresh-brewed coffee, what is the hypothesis?

(d) Use the Binomial distribution in (b) to find the p-value for the hypothesis in (c). What is your conclusion?

(e) Use the Binomial distribution in (b) to find the 95% Clopper-Pearson (exact) confidence interval of the true proportion p.

(f) It looks like that we can use the Normal approximation for this problem. Please verify the condition and conduct the test for the hypothesis in (c). What is your conclusion?

(g) Shall we use the large sample or the plus-four confidence interval? Compute the 95% confidence interval of your choice.

(h) Do the Binomial distribution and the Normal approximation provide you similar answers?

Subject | Mathematics |

Due By (Pacific Time) | 04/22/2014 09:59 pm |

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