Question

A credit officer believes that monthly account balances are a different amount now than they were a year ago. The mean of all balances in the general population last year was $2,200. This year, a sample of 81 account balances shows an average balance of $2,236 with a sample standard deviation of $135.

Construct a 95% confidence interval for the point estimate of the mean; provide the lower and upper bound estimates (2 decimals). Show your work: (2206.15, 2265.85). How does the confidence interval relate to the decision made to reject the null? Do the results agree?

Answer 1

sample mean, xbar = 2236
sample standard deviation, s = 135
sample size, n = 81
degrees of freedom, df = n - 1 = 80

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 1.99

ME = tc * s/sqrt(n)
ME = 1.99 * 135/sqrt(81)
ME = 29.85

CI = (2236 - 1.99 * 135/sqrt(81) , 2236 + 1.99 * 135/sqrt(81))
CI = (2206.15 , 2265.85)

Here, decision is to reject the null because confidence interval does not contain 2200 hpothesised value