Question

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 35 homes in casper, wyoming is $349,237. assume the population standard deviation is $152,867. the mean home sales price for 41 homes in cheyenne, wyoming is $435,244. assume the population standard deviation is $137,829. at \\(\alpha = 0.05\\), is there enough evidence to reject the agency’s claim? complete parts (a) through (e).\
\
(a) identify the claim and state \\(h_0\\) and \\(h_a\\).\
what is\
a. \\(z\\) me sales price in casper, wyoming is the same as in cheyenne, wyoming.\
b. \\(=\\) me sales price in casper, wyoming is greater than in cheyenne, wyoming.\
c. \\(\
eq\\) me sales price in casper, wyoming is not the same as in cheyenne, wyoming.\
d. \\(\leq\\) me sales price in casper, wyoming is less than in cheyenne, wyoming.\
let casper, wyoming be sample 1 and let cheyenne, wyoming be sample 2. identify \\(h_0\\) and \\(h_a\\).\
\\(h_0: \mu_1 \\) dropdown \\(\mu_2\\)\
\\(h_a: \mu_1 \\) dropdown \\(\mu_2\\)

Explanation:

The agency's claim is that the mean home sales price in Casper and Cheyenne are the same. For the null hypothesis \( H_0 \), we assume the claim is true, so \( H_0: \mu_1 = \mu_2 \) (where \( \mu_1 \) is the mean for Casper and \( \mu_2 \) for Cheyenne). The alternative hypothesis \( H_a \) is the opposite of the null, so \( H_a: \mu_1
eq \mu_2 \) (since we're testing if there's a difference, not a specific direction unless stated, and the claim is equality so the alternative is inequality). The correct option for the claim is A as it states the means are the same.

Answer:

A. The mean home sales price in Casper, Wyoming is the same as in Cheyenne, Wyoming.
\( H_0: \mu_1 = \mu_2 \)
\( H_a: \mu_1
eq \mu_2 \)