Question

The average price of homes sold in the U.S. in 2013 was $240,000. A sample of 150 homes sold in Chattanooga in 2013 showed an average price of $236,000. It is known that the standard deviation of the population (σ) is $36,000. We are interested in determining whether the average price of homes sold in Chattanooga is significantly less than the national average. Use a significance level of α equal to 0.05.

Answer 1

Solution:
Null hypothesis H0: mean = 240000
Alternate hypothesis Ha: mean <240000
Sample size = 150
Sample mean = 236000
Population standard deviation = 36000
Ztest stat = (236000-240000)/36000/sqrt(150) = -1.36
Here we will use Z test as population standard deviation is known and Sample size is greater than 30
So p-value = 0.0869
As we can see that p-value is greater than alpha value so we can not reject the null hypothesis. So we can say that we do not have significant evidence to support the alternative hypothesis.