It thanks USA Today reported that about 47 of the general co

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 997 Chevrolet owners and found that 491 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 alpha = 0.01. Solve the problem using both the traditional method and the rho-value method. Since the sampling distribution of p 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.) State your conclusion in context of the application. Compare your conclusion with the conclusion obtained by using the rho-value method. Are they the same?

Solution

Proportion p =0.47 , q =1-0.47 = 0.53

Sample proportion P = 491/997 = 0.49

z = (P-p)/sqrt(pq/n)

= (0.49 - 0.47)/sqrt((0.47*0.53)/997)

= 1.27

Test Static = 1.27 Answer

Critical value = 0.01

P-value = 1 - 0.8980 = 0.102 Answer

Since , P-value > 0.01

Failed to reject null hypothesis , there is insufficient evidence at the 0.01 level to conclude that the true proportions of consumers loyal to the car company is more than 47%.

The conclusions obtained by using both methods are he same.