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 Ford Motor Company did a study of a random sample of 1006 Ford owners and found that 490 said they would buy another Ford. Does this indicate that the population proportion of consumers loyal to Ford is more than 47%? Make conclusions at a 10% level of significance.

a) State the hypotheses to be tested.

b) Calculate and show the test statistic by hand.

c) Calculate the p-value using tables and illustrate the p-value by providing a graph showing appropriate area under the normal curve.

d) Confirm your results using Excel. Show Output.

e) Give your conclusions in a well-written sentence.

Answer 1

Given That: X=490, n=1006, Alpha=0.10
a) To test the Hypothesis,
Ho: p <= 0.47
Ha: p > 0.47 (claim)

b) The Test statistics,

P^=490/1006 = 0.49
test statistic: z = (0.49-0.47)/sqrt[0.47*0.53/1006] = 1.27

c) p-value = P(z > 1.27) = 0.1019

e)Conclusion: Since the p-value is greater than 10%, fail to reject Ho. The test supports the claim at the 5% level
of significance.