9.70 Protecting the environment? When the 2000 General Social Survey asked, "Would you be willing to pay much higher taxes in order to protect the

9.70 Protecting the environment?          When the 2000 General Social Survey asked, "Would you be willing to pay much higher taxes in order to protect the environment?" (variable GRNTAXES), 369 people answered yes and 483 answered no. (We exclude those who made other responses.) Let p denote the population proportion who would answer yes. MINITAB shows the following results to analyze whether a majority or minority of Americans would answer yes:

Test of p=0.5 vs p not =0.5

 X           N          Sample p                    95% CI                         Z-Value                               P-Value

369        852        0.433099             (0.3998, 0.4663)              -3.91                      0.0000

a. What are the assumptions for the significance test? Do they seem to be satisfied for this application? Explain.

b. For this printout, specify the null and alternative hypotheses that are tested, and report the point estimate of p and the value of the test statistic.

 c. Report and interpret the P-value in context.

d. According to the P-value, is it plausible that p=0.50? Explain.

e. Explain an advantage of the confidence interval shown over the significance test.