A Single Population Mean Using the Student's t-Distribution · Exercise 30

The Federal Election Commission (FEC) collects information about campaign contributions and disbursements for candidates and political committees during 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 operated during the 2011–2012 election cycle. The following table shows the total receipts during this cycle for a random selection of 20 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 the sample data to construct a 96 percent confidence interval for the mean amount of money raised by all Leadership PACs during the 2011–2012 election cycle. Use the Student's t-distribution.

OpenStax, Statistics · §8.2 A Single Population Mean Using the Student's t-Distribution · Exercise 30