Question: More confidence interval mistakes and misunderstandings. Suppose 100 randomly selected members of MySpace Karaoke were asked how much time they typically spend on the site during the week. The sample mean \((\bar{x})\) was found to be 4.2 hours. Assume that the population standard deviation is known to be \(\sigma=2.5\).

1. Cary Oakey computes the \(95 \%\) confidence interval for the average time on the site as \(4.2 \pm 1.96 (2.5 / 100) .\) What is his mistake?
2. He corrects this mistake and then states " \(95 \%\) of the members spend between 3.71 and 4.69 hours a week on the site." What is wrong with his interpretation of this interval?
3. The margin of error is slightly less than a half hour. To reduce this down to 15 minutes, Gary says the sample size needs to be doubled to 200. What is wrong with this statement?

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