Question

n Hamilton County, Ohio the mean number of days needed to sell a home is days (Cincinnati Multiple Listing Service, April, 2012). Data for the sale of homes in a nearby country showed a sample mean of days with a sample standard deviation of days. Conduct a hypothesis test to determine whether the mean number of days until a home is sold is different than the Hamilton county mean of days in the nearby county. Round your answer to four decimal places.

Answer 1

Answer:

There is enough evidence to support the claim that the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county.

Test statistic t=-1.8974

P-value = 0.0326

Step-by-step explanation:

The question is incomplete:

"In Hamilton County, Ohio the mean number of days needed to sell a home is 86 days (Cincinnati Multiple Listing Service, April, 2012). Data for the sale of 40 homes in a nearby county showed a sample mean of 80 days with a sample standard deviation of 20 days. Conduct a hypothesis test to determine whether the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county. Round your answer to four decimal places."

This is a hypothesis test for the population mean.

The claim is that the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county.

Then, the null and alternative hypothesis are:

$H_0: \mu=86\\\\H_a:\mu< 86$

The significance level is 0.05.

The sample has a size n=40.

The sample mean is M=80.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=20.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{20}{\sqrt{40}}=3.1623$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{80-86}{3.1623}=\dfrac{-6}{3.1623}=-1.8974$

The degrees of freedom for this sample size are:

$df=n-1=40-1=39$

This test is a left-tailed test, with 39 degrees of freedom and t=-1.8974, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=P(t$

As the P-value (0.0326) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county.