Question

A department store wants to know what fraction of its customers in a certain market have store credit cards, and what their average balance might be.

Of the 120 customers surveyed, 30 had store credit cards. Amongst those customers, the average balance was $600, with a sample standard deviation of $80.

Find the 98% confidence interval for the average credit card balance.

(  ,  ) Round your answers to two decimal places.

Answer 1

sample mean, xbar = 600
sample standard deviation, s = 80
sample size, n = 30
degrees of freedom, df = n - 1 = 29

Given CI level is 98%, hence α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01, tc = t(α/2, df) = 2.462

ME = tc * s/sqrt(n)
ME = 2.462 * 80/sqrt(30)
ME = 35.96

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (600 - 2.462 * 80/sqrt(30) , 600 + 2.462 * 80/sqrt(30))
CI = (564.04 , 635.96)