Question

6. In a sample of 300 houses, the sample average price was found to be $196,340. Assume the variance of house prices is 120,000,000. Let random variable X denote house price, and μ denote its unknown population mean, E(X) = μ. For each of the following questions, formulate the appropriate null and alternative hypotheses, perform the test, and interpret test results:

a. Is the average house price below $200,000?

b. Is the average house price above $200,000?

c. Is the average house price different from $200,000?

Answer 1

Ans:

a)

Test statistic:

z=(196340-200000)/(sqrt(120000000/300))

z=-5.78

P(z<-5.78)=0.0000

As,p-value<0.05,we reject the null hypothesis and we can conclude that mean price is below 200,000.

b)

Test statistic:

z=-5.78

P(z>-5.78)=1.0000

As,p-value>0.05,we fail to reject the null hypothesis and we can not conclude that mean price is above 200,000.

c)

Test statistic:

z=-5.78

p-value=0.0000

As,p-value<0.05,we reject the null hypothesis and we can conclude that mean price is different from 200,000.