Question

One local hockey team conducts a study to compare the amount of money spent on refreshments at the Bell Centre. Two simple random samples of 100 men and 100 women are collected. For men, the average expenditure was $20, with a known population standard deviation of $5. For women, it was $30, with a known population standard deviation of $4.

a) Estimate the difference in the expenditure between man and women using a 99% confidence interval.

b) Based on your confidence interval, do you think there is a significant difference between the expenditure of men and women? Explain.

Answer 1

a)
Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(25/100 + 16/100)
sp = 0.6403

Given CI level is 0.99, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 2.58

CI = (x1bar - x2bar - tc * sp , x1bar - x2bar + tc * sp)
CI = (20 - 30 - 2.58 * 0.6403 , 20 - 30 - 2.58 * 0.6403
CI = (-11.65 , -8.35)

b)
Yes, there is significant difference between the expenditure of men and women.

Because the calculated CI does not contain the 0 within the two bounds.