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.

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