3. 15 points MIntroStat6 8.E.022 My Notes Ask Your Teacher A matched pairs exper

Question

3. 15 points MIntroStat6 8.E.022 My Notes Ask Your Teacher A matched pairs experiment compares 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, 14 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) Test the claim that a majority of people prefer the taste of fresh-brewed coffee. Report the large-sample z statistic. (Round your answer to two decimal places.) Report its P-value. (Round your answer to four decimal places.) (b) Draw a sketch of a standard Normal curve and mark the location of your z statistic. Shade the appropriate area that corresponds to the P-value. -3 -2 2 3 -32 2 3

Explanation / Answer

Answer to the question is as follows:

a. p = 1-14/40 = .65

H0: p<=.5
Ha: p>.5

Z = (.65-.5)/sqrt(.5*.5/40) = 1.90

p-value for Z = +1.90 is P(Z>=+1.90) = .0287

c. Since it is less than .05 the result is significant

Practical conclusion: 2nd option is right , the hypothesis is based on fresh-brewed coeffee

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