A local church has a congregation consisting of 480 adult members. The church's administrators would like to estimate the average weekly donation per member per week. A random sample of 90 members was found to have an average donation of $56.70 and a standard deviation of $10.50. The 90% confidence interval to estimate the average weekly donation is ______ .

Question

Quizplus · Accepted Answer

The 90% confidence interval for the average weekly donation can be calculated using the formula for the confidence interval of the mean, which is $\bar{x} \pm t_{\alpha/2} \cdot \frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $t_{\alpha/2}$ is the t-score corresponding to the desired confidence level (90% in this case), $s$ is the sample standard deviation, and $n$ is the sample size. Given $\bar{x} = 56.70$, $s = 10.50$, and $n = 90$, and knowing that the t-score for 90% confidence with 89 degrees of freedom (since $n-1 = 89$) is approximately 1.645 (though this value might slightly vary, it's close to the value for a large sample size or using a z-score as an approximation for large n), the calculation yields a confidence interval close to the values in option B, indicating that the average weekly donation is estimated with 90% confidence to be between $55.04 and $58.36.

A Local Church Has a Congregation Consisting of 480 Adult