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. the table 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.
| $3,600 | $1,243,900 | $10,900 | $385,200 | $581,500 |
| $7,400 | $2,900 | $400 | $3,714,500 | $632,500 |
| $391,000 | $467,400 | $56,800 | $5,800 | $405,200 |
| $733,200 | $8,000 | $468,700 | $75,200 | $41,000 |
| $13,300 | $9,500 | $953,800 | $1,113,500 | $1,109,300 |
| $353,900 | $986,100 | $88,600 | $378,200 | $13,200 |
| $3,800 | $745,100 | $5,800 | $3,072,100 | $1,626,700 |
| $512,900 | $2,309,200 | $6,600 | $202,400 | $15,800 |
- Find the point estimate for the population mean.
- Using 95% confidence, calculate the error bound.
- Create a 95% confidence interval for the mean total individual contributions.
- Interpret the confidence interval in the context of the problem.