Question

Anystate Auto Insurance Company took a random sample of 372 insurance claims paid out during a 1-year period. The average claim paid was $1530. Assume σ = $260.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

lower limit	$
upper limit	$

Find a 0.99 confidence interval for the mean claim payment. (Round answers to two decimal places.)

lower limit	$
upper limit	$

Answer 1

a)
sample mean, xbar = 1530
sample standard deviation, σ = 260
sample size, n = 372

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.64

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (1530 - 1.64 * 260/sqrt(372) , 1530 + 1.64 * 260/sqrt(372))
CI = (1507.89 , 1552.11)

b)
Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.58

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (1530 - 2.58 * 260/sqrt(372) , 1530 + 2.58 * 260/sqrt(372))
CI = (1495.22 , 1564.78)