Question

# USA Today reported that about 47% of the general consumer population in the United States is...

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 1007 Chevrolet owners and found that 485 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.)

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

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.47

Ha : p > 0.47

= x / n = 485 / 1007 = 0.4816

P0 = 0.47

1 - P0 = 0.53

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.4816 - 0.47 / [(0.47 * 0.53) / 1007]

= 0.74

P(z > 0.74) = 1 - P(z < 0.74) = 0.2297

P-value = 0.2297