The following quote is from the article “Canadians Are Healthier Than We Are” (Associated Press, May 31, 2006): “The Americans also reported more heart disease and major depression, but those differences were too small to be statistically significant.” This statement was based on the responses of a sample of 5183 Americans and a sample of 3505 Canadians. The proportion of Canadians who reported major depression was given as .082.
a. Assuming that the researchers used a one-sided test with a significance level of .05, could the sample proportion of Americans reporting major depression have been as large as .09? Explain why or why not.
b. Assuming that the researchers used a significance level of .05, could the sample proportion of Americans reporting major depression have been as large as .10? Explain why or why not.