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 α = 0.05, is there enough evidence to reject the agency’s claim? complete parts (a) through (e). ... b. z > c. z < (c) find the standardized test statistic z. z = -2.56 (round to two decimal places as needed.) (d) decide whether to reject or fail to reject the null hypothesis. the p - value is 0.010. (round to three decimal places as needed.) reject h₀ because the p - value is less than or equal to α = 0.05. (e) interpret the decision in the context of the original claim. there enough evidence at the 5% level of significance to the agency’s claim that the mean home sales price in casper, wyoming is in cheyenne, wyoming.

Explanation:

Step1: Analyze the Hypothesis Test Result

We rejected the null hypothesis (\(H_0\)) since the P - value (0.010) is less than \(\alpha = 0.05\). The null hypothesis was that the mean home sales prices in Casper and Cheyenne are the same (the agency's claim). Rejecting \(H_0\) means we have enough evidence to dispute the agency's claim.

Step2: Fill in the Blanks

• For the first blank: Since we rejected \(H_0\), there is enough evidence.
• For the second blank: We reject the agency's claim, so the word is reject.
• For the third blank: The agency's claim was that the mean home sales price in Casper is the same as in Cheyenne, so the word is the same (but since we rejected the claim, the context is that we have evidence to say it's not the same, but the structure here is about the original claim's statement. Wait, no - the original claim is \(H_0\): \(\mu_1=\mu_2\) (mean in Casper = mean in Cheyenne). We rejected \(H_0\), so there is enough evidence to reject the claim that they are the same. So the first blank: "is", second: "reject", third: "the same" (because the original claim was that they are the same, and we have evidence to reject that claim).

Answer:

There \(\boldsymbol{\text{is}}\) enough evidence at the 5% level of significance to \(\boldsymbol{\text{reject}}\) the agency’s claim that the mean home sales price in Casper, Wyoming is \(\boldsymbol{\text{the same}}\) in Cheyenne, Wyoming.