USA Today reported that about 47 of the general consumer pop

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 983 Chevrolet owners and found that 492 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 a = 0.01. Solve the problem using both the traditional method and the P-value method. Since the sampling distribution of ?3 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 =

Solution

hypothesis:

Ho: u>47%

Ha: u <47%

p = 492/983 = 0.5005

standard error = sqrt(p (1-p)/n)

= (492/983 * 491/983 * 1/983)

= 0.01595

test static = 0.47 - 0.5005/0.01595

= -1.91

critical value :

this is a left tailed test

critical value = 1.65

p- Value = 0.0279