Question

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 ______________.

Answer 1

Its two tailed test.

Critical value =1.96

Test Statistics = -0.451

P value = 0.6523

At 5 % los there is no significant evidence to reject null hypothesis.

Margin of error = 0.107

IAM 95 % confident that the true population proportion of individual who prefer color blue is between 0.107 and 0.322

PL??