The Public Policy Institute conducts statewide surveys (across California) to collect information about a variety of topics (health, environment, political attitudes, education). In July 2015, PPIC conducted a survey to gather information about the perceived onset of global warming among Californian voters. They asked the following question: Which of the following statements reflects your view of when the effects of global warming will begin to happen? Below is the percentage of the 1,300 respondents that believe the effects of global warming have already begun. We also report results broken out by race. All Adults Asian Black Latino White % responding "already begun" 64% 62% 64% 67% 55% % of total respondents 100% 11% 8% 33% 46%
Consider first the overall result (all voters). Let p be the fraction of Californian voters that believe that global warming has already begun.
1. Use the survey results to estimate p. Also estimate the standard error of your estimate.
2. Construct a 99% confidence interval for p. Interpret.
3. Construct a 95% confidence interval for p. Is it larger or narrower than the 99% confidence interval? Why?
4. Is there statistical evidence that less than 60% of White adults believe that global warming has begun (to answer this question, use the 5 steps for hypothesis testing using a 5% significance level)
5. Is there statistical evidence that the Latino adults are more likely to believe that global warming has begun than Asian adults? Explain (to answer this question use the 5 steps for hypothesis testing)