Statistics Question

Question

USA Today reported that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice. Suppose Chevrolet did a study of a random sample of 1002 Chevrolet owners and found that 487 said they would buy another Chevrolet. Does this indicate that the population proportion of consumers loyal to Chevrolet is more than 47%? Use α = 0.01.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

Find the P-value of the test statistic. (Round your answer to four decimal places.)

Answer 1

Ho: p = 0.47

Ha: p > 0.47

sample proportion (phat) = 487/1002 = 0.486

test statistic z = (0.486-0.47)/(0.47*0.53/1002)**0.5 = 1.015

for right tailed test, p-value = P(z > 1.015). Because normal distribution symmetric that is equal to P(z < -1.015 = 0.155.

Because p-value exceeds 0.01, we do not reject the null hypothesis and we do not have sufficient evidence that the proportion of customers loyal to Chevrolet is greater than 47%.