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 987 Chevrolet owners and found that 494 said they would buy another Chevrolet. Does this indicate that the population proportion of consumers loyal to the car company is more than 47%? Use α = 0.01. Solve the problem using both the traditional method and the P-value method. Since the sampling distribution of p̂ is the normal distribution, you can use critical values from the standard normal distribution as shown in the table of critical values of the z distribution. (Round the test statistic and the critical value to two decimal places. Round the P-value to four decimal places.)

test statistic =

critical value =

P-value =

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.47
Alternative Hypothesis, Ha: p > 0.47

Rejection Region
This is right tailed test, for α = 0.01
Critical value of z is 2.33.
Hence reject H0 if z > 2.33

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.5005 - 0.47)/sqrt(0.47*(1-0.47)/987)
z = 1.92

P-value Approach
P-value = 0.0274
As P-value >= 0.01, fail to reject null hypothesis.