Question

You want to compare housing prices in your community (measured in thousands of dollars) to the national values of µ= 496, σ= 36.3. Recently, 4 houses on your street were sold for a mean price of 476. Report the standard error of the mean and Z in your answers to the following questions.
Can you conclude that the mean price of housing in your community is different from the national mean at a statistically significant level?
How would your conclusion from a. change if you had obtained a sample of n= 81 with a mean of 483?
How would your conclusion from b. change if you realized that actually σ= 96.3?

Answer 1

We can conduct a hypothesis test for the population mean. we have

n = 4

We want to test whether the mean price differs with the national avg. price. We have the population SD so we can use normal z-test. It is a 2-tailed test.

Test Stat =

standard error =

= 18.15

Test Stat= (476 - 496) / 18.15

= -1.1019

Critical value at = 0.05

= 1.96 ..................Using normal percentage tables at p = 0.025

Since |Test Stat| < Critical value

We do not the reject the null hypothesis at 5%. It is not statistically significant and the mean is 496 significantly.

n = 81

Test Stat =

standard error =

= 4.033

Test Stat= (483 - 496) / 4.033

= -3.223

Critical value at = 0.05

= 1.96 ..................Using normal percentage tables at p = 0.025

Since |Test Stat| > Critical value

We reject the null hypothesis at 5%. It is statistically significant and the mean is not 496 significantly.

n = 4

Test Stat =

standard error =

= 48.15

Test Stat= (476 - 496) / 48.15

= -0.4154

Critical value at = 0.05

= 1.96 ..................Using normal percentage tables at p = 0.025

Since |Test Stat| < Critical value

We do not the reject the null hypothesis at 5%. It is not statistically significant and the mean is 496 significantly.