Question

Testing the Difference Between Two Means In Exercises 15–24,
(a) identify the claim and state H0, and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed.

21) Home Prices A real estate agency says that the mean home sales price in Casper, Wyoming, is the same as in Cheyenne, Wyoming. The mean home sales price for 25 homes in Casper is $294,220. Assume the population standard deviation is $135,387. The mean home sales price for 25 homes in Cheyenne is $287,984. Assume the population standard deviation is $151,996. At a = 0.01, is there enough evidence to reject the agency’s claim?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ1 = μ2
Alternative Hypothesis, Ha: μ1 ≠ μ2

b)

Rejection Region
This is two tailed test, for α = 0.01
Critical value of z are -2.576 and 2.576.
Hence reject H0 if z < -2.576 or z > 2.576

c)

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(18329639769/25 + 23102784016/25)
sp = 40709.9122

Test statistic,
z = (x1bar - x2bar)/sp
z = (294220 - 287984)/40709.9122
z = 0.15

d)

fail to reject H0

e)

There is not sufficient evidence to conclude that the mean home sales price in Casper, Wyoming, is the same as in Cheyenne, Wyoming.