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.
p-value= ?
.0652
Z = (score-mean)/SEm
SEm = SD/√n
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability of the Z score.
To conduct a hypothesis test, we need to set up the null hypothesis (H0) and the alternative hypothesis (Ha).
The null hypothesis assumes that there is no difference between the mean number of days until a home is sold in the nearby county and the Hamilton county mean of 86 days. The alternative hypothesis assumes that there is a difference between the means.
H0: The mean number of days until a home is sold in the nearby county is equal to 86 days.
Ha: The mean number of days until a home is sold in the nearby county is different from 86 days.
Next, we calculate the test statistic, which is the z-value. We use the formula:
z = (x̄ - μ) / (σ / √n)
Where:
x̄ = sample mean (80 days)
μ = population mean (86 days)
σ = population standard deviation (given as 20 days)
n = sample size (40 homes)
Plugging in the values, we get:
z = (80 - 86) / (20 / √40)
Now, we can calculate the z-value.