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

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 1006 Chevrolet owners and found that 490 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.
Please provide the following information:
(a) What is the level of significance? State the null and alternate hypotheses.
(b) What sampling will you use? Do you think the sample size is sufficiently large? Explain. Compute the value of the sample test statistic.
(c) Find the P-value of the test statistic. Sketch the sampling and show the area corresponding to the P-value.
(d) Based on your answers in parts (a)–(c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(e) Interpret your conclusion in the context of the application.
Distribution
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