According to the National Association of Realtors, it took an average of three weeks to sell a home in 2017. Suppose data for the sale of 39 randomly selected homes sold in Greene County, Ohio, in 2017 showed a sample mean of 3.6 weeks with a sample standard deviation of 2 weeks. Conduct a hypothesis test to determine whether the number of weeks until a house sold in Greene County differed from the national average in 2017. Use α = 0.05 for the level of significance, and state your conclusion. a. State the null and alternative hypothesis.
b. Find the value of the test statistic.
c. Find the p-value.
d. State your conclusion.

Solution :

Here, given :

Sample size, n = 39

Sample mean, = 3.6

Standard deviation of the sample, s =2

The population mean,

The significance level,

a). Therefore the hypothesis is :

b). The test statics is given as :

     = 1.873

c). The p- value is given by :

d). The conclusion :

  In this case, the p-value is

So, we do not reject .

Therefore, we conclude that it is not a statistically significant difference between national average time for selling a home and the mean time for selling in Greene County.

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step-by-step explanation: