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. the critical value is z₀ = . what is the rejection region? select the correct choice below and fill in the answer box(es) within your choice. (round to two decimal places as needed.) a. z < -1.96 or z > 1.96 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.) h₀ because the p - value is α = 0.05.

Explanation:

Step1: Recall Hypothesis Testing Decision Rule

In hypothesis testing, we reject the null hypothesis \( H_0 \) if the P - value is less than the significance level \( \alpha \), or if the test statistic falls in the rejection region. Here, \( \alpha = 0.05 \) and the P - value is 0.010.

Step2: Compare P - value and \( \alpha \)

We compare the P - value (0.010) with \( \alpha=0.05 \). Since \( 0.010<0.05 \), we reject the null hypothesis. Also, the test statistic \( z = - 2.56 \), and the rejection region is \( z < - 1.96 \) or \( z>1.96 \). Since \( - 2.56 < - 1.96 \), the test statistic is in the rejection region, which also leads us to reject \( H_0 \).

Answer:

Reject \( H_0 \) because the P - value is less than \( \alpha = 0.05 \).