Just before the presidential election in November 2016, a local newspaper conducted a poll of registered voters in a large city and found that 120 out of a random sample of 250 men intended to vote for Donald Trump and 132 out of a random sample of 240 women intended to vote for Donald Trump.
(a) Is there convincing evidence that there is a difference in the proportion of all men and the proportion of all women in this city who intended to vote for Trump at the Ě‘ = 0.05 significance level?
(b) Based on your conclusion in part (a), which mistake, a Type I error or a Type II error, could you have made? Interpret this error in context?
(c) A 95% confidence interval for the difference (men – women) in the proportion of all men and the proportion of all women in this city who intended to vote for Trump is (-0.158, 0.018). Based upon the interval, is there convincing evidence to support the claim that a greater proportion of women than men intended to vote for Trump?
(d) Give one way to increase the power of the test other than increasing the sample sizes. What is a drawback of making that change?