Suppose a large insurance company wants to estimate the difference between the average amount of term life insurance purchased per family and the average amount of whole life insurance purchased per family. To obtain an estimate, one of the company’s actuaries randomly selects 27 families who have term life insurance only and 29 families who have whole life policies only. Each sample is taken from families in which the leading provider is younger than 45 years of age. Use the data obtained to construct a 95% confidence interval to estimate the difference in means for these two groups. Assume the amount of insurance is normally distributed.
Term ..... Whole Life
nT = 27 ..... nW = 29
x̄T = $75,000 ... x̄W = $45,000
sT = $22,000 .... sW = $15,500