A matched pairs experiment compares the taste of instant with fresh-brewed coffe

Question

A matched pairs experiment compares the taste of instant with 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 70 subjects who participate in the study, 28 prefer the instant coffee. Let pbe 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.

(c)

Is your result significant at the 5% level?

YesNo    

What is your practical conclusion?

The result is significant at the 5% level, so we reject H0 and conclude that a majority of people prefer fresh-brewed coffee.The result is not significant at the 5% level, so we do not reject H0 and conclude that a majority of people prefer instant coffee.    The result is significant at the 5% level, so we reject H0 and conclude that a majority of people prefer instant coffee.The result is not significant at the 5% level, so we do not reject H0 and conclude that a majority of people prefer fresh-brewed coffee.The result is not significant at the 5% level, so we reject H0 and conclude that a majority of people prefer instant coffee.

Explanation / Answer

a)
Proportion of people prefer fresh brewed coffee p = 42/70 = 0.6

Below are the null and alternate hypothesis
H0: p <= 0.5
H1: p > 0.5

Test statistics, z = (0.6 - 0.5)/(sqrt(0.5*0.5/70)) = 1.6733

p-value = 0.0471 (use standard z table to get the value)

b)
Graph B is correct

c)
Yes result is significant at 5% level.
The result is significant at the 5% level, so we reject H0 and conclude that a majority of people prefer fresh-brewed coffee.

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