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 hypotheses 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.

Question

Mathematics

Will Harris

18 January, 17:22

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 hypotheses 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.

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Malia Fernandez · Answer 1

Test statistic is - 1.8975

The mean number of days until a home is sold is not different than the Hamilton county mean of 86 days in the nearby county.

Step-by-step explanation:

Null hypothesis: The mean number of days until a home is sold in the nearby county is the same as Hamilton county.

Alternate hypothesis: The mean number of days until a home is sold in the nearby county is different from Hamilton county.

Z = (sample mean - population mean) : sd/√n

sample mean = 80 days

population mean = 86 days

sd = 20 days

n = 40

Z = (80 - 86) : 20/√40 = - 6 : 3.162 = - 1.8975

Assuming a 0.05 significance level, the critical value for a two-tailed test lies between - 1.96 and 1.96

Conclusion: Since the test statistic - 1.8975 falls within the region bounded by - 1.96 and 1.96, fail to reject the null hypothesis