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). 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 (round to three decimal places as needed.)

Explanation:

Step1: Recall P - value formula for two - tailed test

For a two - tailed z - test, the P - value is the probability that \(Z < -|z|\) or \(Z > |z|\), where \(z\) is the standardized test statistic. Given \(z=- 2.56\), so \(|z| = 2.56\).
We can use the standard normal distribution table (or a calculator with normal distribution functions) to find the area to the left of \(z=-2.56\) and double it (since it's a two - tailed test).
The cumulative distribution function of the standard normal distribution \(P(Z < - 2.56)\) can be found from the z - table. Looking up \(z = - 2.56\) in the standard normal table, we know that \(P(Z < - 2.56)=0.0052\) (using more precise calculation or table values).
Since it's a two - tailed test, the P - value \(=2\times P(Z < - 2.56)\)

Step2: Calculate the P - value

\(P - value=2\times0.0052 = 0.0104\approx0.010\) (rounded to three decimal places)

Answer:

\(0.010\)