91Ó°ÊÓ

Determine the critical value \(z_{\alpha / 2}\) that corresponds to the given level of confidence. \(98 \%\)

A simple random sample of size \(n\) is drawn from a population that is known to be normally distributed. The sample variance, \(s^{2}\) is determined to be 12.6 . (a) Construct a \(90 \%\) confidence interval for \(\sigma^{2}\) if the sample size, \(n,\) is 20 (b) Construct a \(90 \%\) confidence interval for \(\sigma^{2}\) if the sample size, \(n\), is \(30 .\) How does increasing the sample size affect the width of the interval? (c) Construct a \(98 \%\) confidence interval for \(\sigma^{2}\) if the sample size, \(n\), is 20. Compare the results with those obtained in part (a). How does increasing the level of confidence affect the width of the confidence interval?

Construct the appropriate confidence interval. A simple random sample of size \(n=12\) is drawn from a population that is normally distributed. The sample variance is found to be \(s^{2}=23.7\). Construct a \(90 \%\) confidence interval for the population variance.

Determine the point estimate of the population proportion, the margin of error for each confidence interval, and the number of individuals in the sample with the specified characteristic, \(x,\) for the sample size provided. Lower bound: \(0.201,\) upper bound: \(0.249, n=1200\)

Travelers pay taxes for flying, car rentals, and hotels. The following data represent the total travel tax for a 3-day business trip in eight randomly selected cities. Note: Chicago has the highest travel taxes in the country at 101.27 dollar. In Problem 32 from Section \(9.2,\) it was verified that the data are normally distributed and that \(s=12.324\) dollars. Construct and interpret a \(90 \%\) confidence interval for the standard deviation travel tax for a 3 -day business trip. $$ \begin{array}{llll} \hline 67.81 & 78.69 & 68.99 & 84.36 \\ \hline 80.24 & 86.14 & 101.27 & 99.29 \\ \hline \end{array} $$

A simple random sample of size \(n<30\) for \(a\) quantitative variable has been obtained. Using the normal probability plot, the correlation between the variable and expected z-score, and the boxplot, judge whether a t-interval should be constructed. $$ n=9 ; \text { Correlation }=0.997 $$

Determine the point estimate of the population mean and margin of error for each confidence interval. Lower bound: \(18,\) upper bound: 24

Determine the point estimate of the population mean and margin of error for each confidence interval. Lower bound: \(20,\) upper bound: 30

Determine the point estimate of the population proportion, the margin of error for each confidence interval, and the number of individuals in the sample with the specified characteristic, \(x,\) for the sample size provided. Lower bound: \(0.853,\) upper bound: \(0.871, n=10,732\)

Construct a confidence interval of the population proportion at the given level of confidence. \(x=30, n=150,90 \%\) confidence