Question: A simple random sample of size \(n\) is drawn from a population whose population standard deviation, \(\sigma\), is known to be 3.8. The sample mean, \(\bar{x}\), is determined to be 59.2.

1. Compute the \(90 \%\) confidence interval for \(\mu\) if the sample size, \(n\), is 45 .
2. Compute the \(90 \%\) confidence interval for \(\mu\) if the sample size, \(n\), is 55. How does increasing the sample size affect the margin of error, \(E\) ?
3. Compute the \(98 \%\) confidence interval for \(\mu\) if the sample size, \(n\), is 45 . Compare the results to those obtained in
   part (a). How does increasing the level of confidence affect the size of the margin of error, \(E\) ?
4. Can we compute a confidence interval for \(\mu\) based on the information given if the sample size is \(n=15\) ? Why? If the sample size is \(n=15\), what must be true regarding the population from which the sample was drawn?

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