Question

Suppose a Realtor is interested in comparing the asking prices of midrange homes in Peoria, Illinois, and Evansville, Indiana. The Realtor conducts a small telephone survey in the two cities, asking the prices of midrange homes. A random sample of 21 listings in Peoria resulted in a sample average price of $116,900, with a standard deviation of $2,300. A random sample of 26 listings in Evansville resulted in a sample average price of $114,000, with a standard deviation of $1,750. The Realtor assumes prices of midrange homes are normally distributed and the variance in prices in the two cities is about the same. The researcher wishes to test whether there is any difference in the mean prices of midrange homes of the two cities for α= 0.01. The null hypothesis for this problem is ______.

a. μ1 - μ2 < 0
b. μ1 - μ2 > 0
c. μ1 - μ2 = 1
d. μ1 - μ2 ≠ 0
e. μ1 - μ2 = 0

Answer 1

For this case we want to test if there is any difference in the mean prices of midrange homes of the two cities so then the system of hypothesis are:

Null hypothesis:
`\mu_1 -\mu_2 =0`

Alternative hypothesis:
`\mu_1 -\mu_2 \\eq 0`

And the best option for this case would be:

e. μ1 - μ2 = 0

And we can test the hypothesis using a two sample t test for the means

Explanation:

For this case we have the following info given:

`\bar X_1 = 116900` represent the sample mean for Peoria

`s_1 = 2300` represent the sample deviation

`n_1 = 21` represent the sample size for Peoria

`\bar X_2 = 114000` represent the sample mean for Evansville

`s_2 = 1750` represent the sample deviation

`n_2 = 26` represent the sample size for Evansville

For this case we want to test if there is any difference in the mean prices of midrange homes of the two cities so then the system of hypothesis are:

Null hypothesis:
`\mu_1 -\mu_2 =0`

Alternative hypothesis:
`\mu_1 -\mu_2 \\eq 0`

And the best option for this case would be:

e. μ1 - μ2 = 0

And we can test the hypothesis using a two sample t test for the means