Do political “attack ads” work? A congressional candidate who currently has the support of only 44% of the voters runs a television spot that aggressively attacks the character of his opponent. He wants to know if the television spot has changed his support level among voters. (a) Define the parameter and state the null and alternative hypotheses for this test. (b) Suppose his pollsters plan to survey a random sample of 450 voters and conduct a two-sided test ofH0: p = 0.44, using = 0.05. They determine that the power of this test against the alternative p = 0.40 is 0.36. Explain what this means in the context of the problem. (c) Describe two ways the pollsters can increase the power of the test. (d) The pollsters survey a random sample of 450 voters and find that 186 support the candidate. This produces a 95% confidence interval for the proportion of voters who support him of (0.368, 0.459). Use the confidence interval to determine whether this test would reject or fail to reject the null hypothesis. Explain your reasoning.
Do political “attack ads” work? A congressional candidate who currently has the support of only 44% of the
voters runs a television spot that aggressively attacks the character of his opponent. He wants to know if the
television spot has changed his support level among voters.
(a) Define the parameter and state the null and alternative hypotheses for this test.
(b) Suppose his pollsters plan to survey a random sample of 450 voters and conduct a two-sided test ofH0: p =
0.44, using = 0.05. They determine that the power of this test against the alternative p = 0.40 is 0.36.
Explain what this means in the context of the problem.
(c) Describe two ways the pollsters can increase the power of the test.
(d) The pollsters survey a random sample of 450 voters and find that 186 support the candidate. This
produces a 95% confidence interval for the proportion of voters who support him of (0.368, 0.459). Use
the confidence interval to determine whether this test would reject or fail to reject the null hypothesis.
Explain your reasoning.
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