A matched pairs experiment compares the taste of instant coffee 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 50 subjects who participate in the study, 19 prefer the instant coffee and the other 31 prefer fresh-brewed. Let p be the proportion of the population that prefers fresh-brewed coffee. a. Test the claim that a majority of people prefer the taste of fresh-brewed coffee. Report the z test-statistic and its p-value. Is your test result significant at the α = 10% level? What is your practical conclusion? b. compute the hypothesis testing with significance level a=10%. Use the data set above. c. Find a 95%(not 90%) confidence interval for population proportion p. Solution: Population: {Xi = 1} → Customer i prefers fresh-brewed coffee to instant coffee p = the proportion of the population that prefers fresh-brewed coffee. Hypotheses (UPPER, LOWER, or TWO-Tailed TEST) with ? = 10%: Ho: ? = p0 = 0.50 vs. Ha: ? < 0.50 or ? > 0.50 or ? ≠ 0.50 (circle one) Sample: Sample size: n = 50 Data: Count: X = X1 + X2 +…+ X50 = 31 X = Count how many customers prefers fresh-brewed coffee to instant coffee; X~ Binomial (n = 50, p = ??? ) • From Sample Data: Sample PROPORTION (statistic): ?̅ = ? ? =____________ • Step 1: Hypotheses (???-TAILED) TEST): H0: p = p0 = 0.0 vs. HA: p < 0.50 or p > 0.50 or p ≠ 0.50 (circle one) • ASSUME Ho IS TRUE: p = po = 0.50 • Standard Error: ???? = √ ?? ( ?− ?? ) ? = _________________________ • Step 2: Test Statistic: z = ?̅ − ?? ???? = _____________________________ • Step 3: p-value = P(Z _________ ) = __________________________ (Use z-Table) • Step 4: Conclusion: DO NOT REJECT H0 or REJECT H0 (circle one) • Interpretation of the conclusion (circle one) based: a. The percentage of customers who prefer fresh-brewed coffee is NOT “SIGNIFICANTLY” MORE THAN that of instant coffee. b. The percentage of customers who prefer fresh-brewed coffee is “SIGNIFICANTLY” MORE THAN that of instant coffee. • OUTPUT for the significance test above: p-value = _______________________ • Find the 95% confidence interval (not 90%) (watch out: use 2-tailed test): Confidence Interval = [ _________, __________]
A matched pairs experiment compares the taste of instant coffee 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 50 subjects who participate in the study, 19 prefer the instant coffee and the other 31 prefer fresh-brewed.
Let p be the proportion of the population that prefers fresh-brewed coffee.
a. Test the claim that a majority of people prefer the taste of fresh-brewed coffee. Report the z test-statistic and its p-value. Is your test result significant at the α = 10% level? What is your practical conclusion?
b. compute the hypothesis testing with significance level a=10%. Use the data set above.
c. Find a 95%(not 90%) confidence interval for population proportion p.
Solution:
Population: {Xi = 1} → Customer i prefers fresh-brewed coffee to instant coffee
p = the proportion of the population that prefers fresh-brewed coffee. Hypotheses (UPPER, LOWER, or TWO-Tailed TEST) with ? = 10%:
Ho: ? = p0 = 0.50 vs.
Ha: ? < 0.50 or ? > 0.50 or ? ≠ 0.50 (circle one)
Sample:
X = Count how many customers prefers fresh-brewed coffee to instant coffee; X~ Binomial (n = 50, p = ??? )
• From Sample Data: Sample PROPORTION (statistic): ?̅ = ? ? =____________
• Step 1: Hypotheses (???-TAILED) TEST): H0: p = p0 = 0.0 vs. HA: p < 0.50 or p > 0.50 or p ≠ 0.50 (circle one)
• ASSUME Ho IS TRUE: p = po = 0.50
• Standard Error: ???? = √ ?? ( ?− ?? ) ? = _________________________
• Step 2: Test Statistic: z = ?̅ − ?? ???? = _____________________________
• Step 3: p-value = P(Z _________ ) = __________________________ (Use z-Table) • Step 4: Conclusion: DO NOT REJECT H0 or REJECT H0 (circle one)
• Interpretation of the conclusion (circle one) based:
a. The percentage of customers who prefer fresh-brewed coffee is NOT “SIGNIFICANTLY” MORE THAN that of instant coffee.
b. The percentage of customers who prefer fresh-brewed coffee is “SIGNIFICANTLY” MORE THAN that of instant coffee.
• OUTPUT for the significance test above: p-value = _______________________
• Find the 95% confidence interval (not 90%) (watch out: use 2-tailed test): Confidence Interval = [ _________, __________]
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