Question

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. Useα = 0.05for the level of significance, and state your conclusion.(a)State the null and alternative hypothesis. (Enter != for ≠ as needed.)H0:_____________Ha:__________(b)Find the value of the test statistic. (Round your answer to three decimal places.)Find the p-value. (Round your answer to four decimal places.)p-value =___________.

Answer 1

1.8732, 0.068

Explanation:

Given that according to the National Association of Realtors, it took an average of three weeks to sell a home in 2017.

Sample size n = 39

a)
`\bar x = 3.6\\s = 2`

Std error of sample =
`(2)/(√(39) ) \\=0.3203`

`H_0: \bar x = 3\\H_a: \bar x \\eq 3`

(Two tailed test at 5% significance level)

Mean difference = 0.6

Since population std deviation is not known, t test to be used.

b) Test statistic t = mean diff/std error =
`(0.6)/(0.3203 ) \\=1.8732`

df = 38

c) p value = 0.068