Question

Coquitlam Builders is a medium size home construction company. It wants to test the hypothesis that the average size of a new home unit exceeds 2,400 square feet. A random sample of 36 newly constructed homes had a mean of 2,510 square feet. Assume that the standard deviation of the size for all newly constructed homes is 480 square feet. Toll Brothers would like to set α = 0.02. Using the confidence interval approach, what is the decision in this case?

Answer 1

H0: mu = 2400
Ha: mu > 2400

Here, as the hypothesis test is right tailed (one tailed test) we need to calculate the CI for 1 - 2*alpha = 96% CI

sample mean, xbar = 2510
sample standard deviation, σ = 480
sample size, n = 36

Given CI level is 96%, hence α = 1 - 0.96 = 0.04
α/2 = 0.04/2 = 0.02, Zc = Z(α/2) = 2.05

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (2510 - 2.05 * 480/sqrt(36) , 2510 + 2.05 * 480/sqrt(36))
CI = (2346 , 2674)

As the value of 2400 lies below the upper bound of the CI, we fail to reject the null hypothesis and conclude that there is not signficant evidence that the average size of new home unit exceeds 2400 square feet