6.13 Public option, Part I: A Washington Post article from 2009 reported that "support for a government-run health-care plan to compete with private insurers has rebounded from its summertime lows and wins clear majority support from the public." More specifically, the article says "seven in 10 Democrats back the plan, while almost nine in 10 Republicans oppose it. Independents divide 52 percent against, 42 percent in favor of the legislation." (6% responded with "other".) There were 819 Democrats, 566 Republicans and 783 Independents surveyed. (a) A political pundit on TV claims that a majority of Independents oppose the health care public option plan. Do these data provide strong evidence to support this statement? Write the hypotheses used to test the pundit's statement:

• H₀: p_{independent against} = .5 H_a: p_{independent against} = .52
• H₀: p_{independent against} = .5 H_a: p_{independent against} > .5
• H₀: p_{independent against} = .52 H_a: p_{independent against} < .52

What is the p-value associated with this hypothesis test? (please round to four decimal places) What is the conclusion of the hypothesis test?

• Since p< we reject the null hypothesis and accept the alternative
• Since p we do not have enough evidence to reject the null hypothesis
• Since p< we fail to reject the null hypothesis
• Since p we accept the null hypothesis
• Since p we reject the null hypothesis and accept the alternative

The meaning of this conclusion in the context of our investigation is:

• The data does not provide strong evidence to support the pundit's statement
• The data provide strong evidence to support the pundit's statement

(b) Would you expect a confidence interval for the proportion of Independents who oppose the public option plan to include 0.5? Explain.

• Yes
• No