# Question

In the United States, historically, 40% of registered voters are Republican. Suppose you obtain a simple random sample of 320 registered voters and ﬁnd 142 registered Republicans.

(a) Consider the hypotheses H0: p = 0.4 versus H1: p < 0.4. Explain what the researcher would be testing. Perform the test at the α = 0.05 level of signiﬁcance. Write a conclusion

for the test.

(b) Consider the hypotheses H0: p = 0.41 versus H1: p < 0.41. Explain what the researcher would be testing. Perform the test at the α = 0.05 level of signiﬁcance. Write a conclusion for the test.

(c) Consider the hypotheses H0: p = 0.42 versus H1: p < 0.42. Explain what the researcher would be testing. Perform the test at the α = 0.05 level of signiﬁcance. Write a conclusion for the test.

(d) Based on the results of parts (a)–(c), write a few sentences that explain the difference between “accepting” the statement in the null hypothesis versus “not rejecting” the statement in the null hypothesis.

(a) Consider the hypotheses H0: p = 0.4 versus H1: p < 0.4. Explain what the researcher would be testing. Perform the test at the α = 0.05 level of signiﬁcance. Write a conclusion

for the test.

(b) Consider the hypotheses H0: p = 0.41 versus H1: p < 0.41. Explain what the researcher would be testing. Perform the test at the α = 0.05 level of signiﬁcance. Write a conclusion for the test.

(c) Consider the hypotheses H0: p = 0.42 versus H1: p < 0.42. Explain what the researcher would be testing. Perform the test at the α = 0.05 level of signiﬁcance. Write a conclusion for the test.

(d) Based on the results of parts (a)–(c), write a few sentences that explain the difference between “accepting” the statement in the null hypothesis versus “not rejecting” the statement in the null hypothesis.

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