A Confidence Interval When the Population Standard Deviation Is Unknown and Small Sample Case · Exercise 30

The Federal Election Commission (FEC) collects information about campaign contributions and disbursements for candidates and political committees each election cycle. A political action committee (PAC) is a committee formed to raise money for candidates and campaigns. A Leadership PAC is a PAC formed by a federal politician (senator or representative) to raise money to help other candidates’ campaigns.
The FEC has reported financial information for 556 Leadership PACs that were operating during a certain election cycle. The following table shows the total receipts during this cycle for a random selection of 30 Leadership PACs.

\begin{array}{|c|c|c|c|c|}\hline \text{$46,500.00} & \text{$0} & \text{$40,966.50} & \text{$105,887.20} & \text{$5,175.00} \\ \hline \text{$29,050.00} & \text{$19,500.00} & \text{$181,557.20} & \text{$31,500.00} & \text{$149,970.80} \\ \hline \text{$2,555,363.20} & \text{$12,025.00} & \text{$409,000.00} & \text{$60,521.70} & \text{$18,000.00} \\ \hline \text{$61,810.20} & \text{$76,530.80} & \text{$119,459.20} & \text{$0} & \text{$63,520.00} \\ \hline \text{$6,500.00} & \text{$502,578.00} & \text{$705,061.10} & \text{$708,258.90} & \text{$135,810.00} \\ \hline \text{$2,000.00} & \text{$2,000.00} & \text{$0} & \text{$1,287,933.80} & \text{$219,148.30} \\ \hline\end{array}
\bar{x} = \ 251, 854.23$
s = \textrm{ } \ 521, 130.41$
Use this sample data to construct a 95% confidence interval for the mean amount of money raised by all Leadership PACs during that specific election cycle. Use the Student's t-distribution.

OpenStax, Introductory Business Statistics 2e · §8.2 A Confidence Interval When the Population Standard Deviation Is Unknown and Small Sample Case · Exercise 30