Chapter 9.3, Problem 12P

For Problems 7-21. please provide the following information.

(a) What is the level of significance? State the null and alternate hypotheses.

(b)Check Requirements What sampling distribution will you use? Do you think the sample size is sufficiently large? Explain. Compute the value of the sample test statistic and corresponding z value.

(c) Find the P-value of the lest statistic. Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c). will you reject or fail to reject the null hypothesis? Are the data statistically significant at level $\alpha$?

(e)Interpret your conclusion in the context of the application.

Preference: Color What is your favorite color? A large survey of countries, including the United States, China, Russia, France. Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color (Reference: Study by J. Bunge and A. Freeman-Gallant. Statistics Center, Cornell University). Suppose a random sample of n = 56 college students were surveyed, and r = 12 of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use $\alpha =0.05$.