Question

A recent report stated that Canadian life expectancy, on average, is 80.7 years —— better than in the United States ( 78.1 years) but not as good as Japan (82.7 year). Assumme that Canadian life expectancies are approximately normal, wih a standard deviation of 9.3 years. A random sample of 35 death certificates drawn from a national Canadian vital statistics database indicated a mean age at death of 79.5 years. (a) (1 point) Find the best point estimate (b) (3 points) Find the 95% confidence interval estimate of the population mean. (c) (2 points) Do these results support the report of average Canadian life expectancy?

Answer 1

a)

best point estimate = 79.5

b)

sample mean, xbar = 79.5
sample standard deviation, σ = 9.3
sample size, n = 35

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

ME = zc * σ/sqrt(n)
ME = 1.96 * 9.3/sqrt(35)
ME = 3.08

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (79.5 - 1.96 * 9.3/sqrt(35) , 79.5 + 1.96 * 9.3/sqrt(35))
CI = (76.4189 , 82.5811)

CI = (76.42 , 82.58) upto 2 decimal
c)

No, because confidence interval contains 80.7 years