Question

1. 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?

5. The ticketing agency of the Vancouver Whitecaps football team would like to test the hypothesis that the average price of a ticket is less than $225 on the secondary market. A random sample of 40 customers paid an average of $207 for their ticket. Assume that the standard deviation of the price of tickets for Whitecaps games is $43. The Vancouver Whitecaps would like to set α = 0.01. Use the p value approach to test this hypothesis. What will be your decision? (3 points)

Answer 1

1)

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

Given CI level is 98%, hence α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01, Zc = Z(α/2) = 2.3263

ME = zc * σ/sqrt(n)
ME = 2.3263 * 480/sqrt(36)
ME = 186.1

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (2510 - 2.3263 * 480/sqrt(36) , 2510 + 2.3263 * 480/sqrt(36))
CI = (2323.9 , 2696.1)

Fail to reject H0 as 2400 is included in th einterval

b)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 225
Alternative Hypothesis, Ha: μ < 225

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (207 - 225)/(43/sqrt(40))
z = -2.65

P-value Approach
P-value = 0.0040
As P-value < 0.01, reject the null hypothesis.