A Single Population Mean using the Normal Distribution · Exercise 44

The Federal Election Commission collects information about campaign contributions and disbursements for candidates and political committees each election cycle. During a certain campaign season, there were 1,619 candidates for the House of Representatives across the United States who received contributions from individuals. shows the total receipts from individuals for a random selection of 40 House candidates rounded to the nearest $100. The standard deviation for this data to the nearest hundred is σ = $909,200.

\begin{array}{|c|c|c|c|c|}\hline \text{$3,600} & \text{$1,243,900} & \text{$10,900} & \text{$385,200} & \text{$581,500} \\ \hline \text{$7,400} & \text{$2,900} & \text{$400} & \text{$3,714,500} & \text{$632,500} \\ \hline \text{$391,000} & \text{$467,400} & \text{$56,800} & \text{$5,800} & \text{$405,200} \\ \hline \text{$733,200} & \text{$8,000} & \text{$468,700} & \text{$75,200} & \text{$41,000} \\ \hline \text{$13,300} & \text{$9,500} & \text{$953,800} & \text{$1,113,500} & \text{$1,109,300} \\ \hline \text{$353,900} & \text{$986,100} & \text{$88,600} & \text{$378,200} & \text{$13,200} \\ \hline \text{$3,800} & \text{$745,100} & \text{$5,800} & \text{$3,072,100} & \text{$1,626,700} \\ \hline \text{$512,900} & \text{$2,309,200} & \text{$6,600} & \text{$202,400} & \text{$15,800} \\ \hline\end{array}

(a) Find the point estimate for the population mean.
(b) Using 95% confidence, calculate the error bound.
(c) Create a 95% confidence interval for the mean total individual contributions.
(d) Interpret the confidence interval in the context of the problem.

OpenStax, Introductory Statistics 2e · §8.1 A Single Population Mean using the Normal Distribution · Exercise 44