A matched pairs experiment compares the taste of instant versus fresh-brewed cof

Question

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 50 subjects who participate in the study, 16 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) 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?

Explanation / Answer

Answer to the question)

Sample Size = 50

who prefer instant coffee = 16

who prefer fresh brew = 50-16 = 34

p = proportion of fresh brew prefers

Sample proprotion P^ = 34/50 = 0.78

.

Null hypothesis: p = 0.5

Alternate hypothesis : p > 0.5

.

z = (p^ - p) / SE

.

SE = sqrt(0.5*0.5/50)

SE = 0.0707

.

On plugging the values we get

z = (0.78 -0.5) / 0.0707

z = 3.96

.

P value = 0.000037

.

Inference: Since the P value < alpha 0.05 , we reject the null

Conclusion: We conclude that there is statistical significance to support the claim that the prooportion of people who prefer fresh-brewed coffee is greater

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.