A certain researcher thinks that the proportion of women who say that the earth is getting warmer is greater than the proportion of men. The research conducted a survey, and found the following result :
In a random sample of 250 women, 70% said that the earth is getting warmer.
In a random sample of 200 men, 67% said that the earth is getting warmer.
Assume we want to use a 0.05 significance level to test the claim.
(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
(c) Determine the critical value. Show all work; writing the correct critical value, without supporting work, will receive no credit.
(d) Is there sufficient evidence to support the claim that the proportion of women saying the earth is getting warmer is higher than the proportion of men saying the earth is getting warmer? Justify your conclusion.