13. With a sample size of 10 and a confidence level of \( 90 \% \), what is the two tailed \( t \)-value?
14. With a sample size of 20 and a confidence level of \( 95 \% \), what is the two tailed \( t \)-value?
15. With a sample size of 30 and a confidence level of \( 99 \% \), what is the two tailed \( t \)-value?
16. Suppose a random sample of 25 employees has been selected from those working in a company and their number of overtime hours last week is recorded. The sample results in a mean of 8.46 and a standard deviation of 3.61 hours. Construct a \( 99 \% \) confidence interval for the population mean.
17. Suppose we create a confidence interval to estimate the average yearly income of doctors. A sample of 30 doctors yielded a mean of \( \$ 145,580 \) and a standard deviation of \( \$ 13,200 \). From this information a \( 95 \% \) confidence interval was formed, ( \( \$ 140,651.59, \$ 150,508.41 \) ). Interpret this confidence interval.