(Solved): sample of size 36 was taken out of a population with population standard eviation of \( \sigma=3 \ ...

sample of size 36 was taken out of a population with population standard eviation of \( \sigma=3 \). The sample mean was calculated to be 20 . a) Construct a \( 95 \% \) confidence interval for the population mean. Do not round. 95\% CI: ( ) b) Construct a \( 98 \% \) confidence interval for the above problem. Do not round. 98\% CI: ( , ) c) Explain how and why the two intervals are different, what happens to the confidence interval if the confidence level is increased? d) Increase the sample size from \( n=36 \) to \( n=56 \). Construct 95\% confidence interval for population mean. Round to the nearest thousandth. 95\% CI, \( n=56:(\ldots) \) e) Explain the resulting difference, what happens to the confidence interval when the sample size is increased?