Question

A survey of nonprofit organizations showed that online fundraising has increased in the last year. Based on a random sample of 50 nonprofits, the mean one-time gift donation in the past year was $30, with a standard deviation of $10.

Construct a 95% confidence interval estimate for the population one-time gift donation.

Answer 1

To construct a 95% confidence interval estimate for the population one-time gift donation, you can use the formula CI = X ± Z * (S / sqrt(n)), where X is the sample mean, Z is the Z-score corresponding to the desired confidence level, S is the sample standard deviation, and n is the sample size. Plugging in the given values, the confidence interval is approximately $27.23 to $32.77.

Step-by-step explanation:

To construct a 95% confidence interval estimate for the population one-time gift donation, we can use the formula:

CI = X ± Z * (S / sqrt(n))

Where CI is the confidence interval, X is the sample mean, Z is the Z-score corresponding to the desired confidence level (in this case, 95% confidence corresponds to a Z-score of 1.96), S is the sample standard deviation, and n is the sample size.

Given that the sample mean one-time gift donation is $30, the sample standard deviation is $10, and the sample size is 50, we can plug these values into the formula:

CI = $30 ± 1.96 * ($10 / sqrt(50))

Calculating the expression inside the parentheses gives:

CI = $30 ± 2.77

Therefore, the 95% confidence interval estimate for the population one-time gift donation is approximately $27.23 to $32.77.