Question

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 65 members was found to have an average donation of $50.40 and a standard deviation of $12.30. The 95% confidence interval to estimate the average weekly donation is ________.

Answer 1

The confidence interval = ($47.41, $53.39)

Explanation:

Confidence Interval formula

= Mean ± z × Standard deviation/√n

Mean = $50.40

Standard deviation = $12.30

z score for a 95% confidence interval = 1.96

n = 65

Confidence Interval = $50.40 ± 1.96 × $12.30/√65

= $50.40 ± 2.9902293815

Confidence Interval =

$50.40 - 2.9902293815 =

47.409770618

≈$47.41

$50.40 + 2.9902293815 = 53.390229381

≈$53.39

Therefore, the confidence interval = ($47.41, $53.39)