Calculus and Above

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What is your favorite...

What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicate 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 56 college students were surveyed and 12 of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different from that of the general population? Use 5% level of significance. a. Identify the underlying distribution and state why. b. State the null hypothesis. c. State the alternative hypothesis. d. Circle one: One Tail Test / Two Tail Test. e. State the critical value for the hypothesis test. f. Illustrate graphically the rejection region.

g. Compute the test statistic.

h. Find the p-value for the test statistic. i. Give the significant statement for the hypothesis test: At the ________ level of significance, there is ______________________ evidence to reject the null hypothesis.

j. State the critical value for the estimation of the confidence interval. k. Construct a 95% confidence interval for the true proportion of people who prefer color blue. i. Margin of error: ii. Confidence Interval:

l. Give the confidence statement for the confidence interval: I am _________ confident that the true ____________________ of individuals who prefer color blue is between ____________ and ______________.

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