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Changes in car insurance premium are analyzed. A group of n = 25 car policies was selected at random. Individual records were presented as pairs {(Xj , Yj ) : 1 ≤ j ≤ 25}, where Xj and Yj represent the premium amounts for a driver j paid in the last and present years, respectively. It is assumed that differences, {Dj = Yj - Xj : 1 ≤ j ≤ 25} are independent and normally distributed with unknown parameters, µ = µD = E [Dj ] and σ = σD = SD [Dj ]. Sample was summarized and summaries were found as Sample Means: X¯ = 560, Y¯ = 632, and sample standard deviation based on individual differences was s = 160.
1. Estimate the population average difference, E [D] at C = 0.95 confidence.
2. At significance level α = 0.05, do you have sufficient evidence that the average premium has increased, or µY > µX? Solution
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