   # In Hamilton County, Ohio, the mean number of days needed to sell a house is 86 days (Cincinnati Multiple Listing Service, April, 2012). Data for the sale of 40 houses 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 house is sold is different than the Hamilton County mean of 86 days in the nearby county. Use α = .05 for the level of significance, and state your conclusion. 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 9, Problem 67SE
Textbook Problem
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## In Hamilton County, Ohio, the mean number of days needed to sell a house is 86 days (Cincinnati Multiple Listing Service, April, 2012). Data for the sale of 40 houses 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 house is sold is different than the Hamilton County mean of 86 days in the nearby county. Use α = .05 for the level of significance, and state your conclusion.

To determine

Test whether the mean number of days until a house is sold is different than the Hamilton County mean of 86 days in the nearby county.

### Explanation of Solution

Calculation:

The given information is that the sample size is n=40, the sample mean is x¯=80, and the sample standard deviation is s=20.

Here, the claim is that the mean number of days until a house is sold is different than the Hamilton County mean of 86 days in the nearby county. This can be written as μ86. The complement of the claim is, μ=86. In the given experiment, the alternative hypothesis indicates the claim.

The null and alternative hypotheses are given below:

Null hypothesis:

H0:μ=86

Alternative hypothesis:

Ha:μ86 (claim)

Test statistic and p-value:

Software Procedure:

Step-by-step procedure to obtain the test statistic using the MINITAB software:

• Choose Stat > Basic Statistics > 1-Sample t.
• In Summarized data, enter the sample size as 40 and mean as 80

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