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 during each election cycle. During the 2012 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 percent confidence, calculate the error bound.
(c) Create a 95 percent confidence interval for the mean total individual contributions.
(d) Interpret the confidence interval in the context of the problem.

OpenStax, Statistics · §8.1 A Single Population Mean Using the Normal Distribution · Exercise 44