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A national television network takes an exit poll of 1400 voters after each has cast a vote in a state gubernatorial election. Of them, 660 say they voted for the Democratic candidate and 740 say they voted for the Republican candidate. a. Treating the sample as a random sample from the population of all voters, would you predict the winner? Base your decision on a \(95 \%\) confidence interval. b. Base your decision on a \(99 \%\) confidence interval. Explain why you need stronger evidence to make a prediction when you want greater confidence.

Wage discrimination? According to a union agreement, the mean income for all senior-level assembly-line workers in a large company equals \(\$ 500\) per week. A representative of a women's group decides to analyze whether the mean income for female employees matches this norm. For a random sample of nine female employees, using software, she obtains a \(95 \%\) confidence interval of ( 371 , 509 ). Explain what is wrong with each of the following interpretations of this interval. a. We infer that \(95 \%\) of the women in the population have income between \(\$ 371\) and \(\$ 509\) per week. b. If random samples of nine women were repeatedly selected, then \(95 \%\) of the time the sample mean income would be between \(\$ 371\) and \(\$ 509\). c. We can be \(95 \%\) confident that \(\bar{x}\) is between \(\$ 371\) and \(\$ 509 .\) d. If we repeatedly sampled the entire population, then \(95 \%\) of the time the population mean would be between \(\$ 371\) and \(\$ 509 .\)