Question

The average cost of a home in the United States is known to be $200,000 with a population standard deviation of $208,935. Suppose we take a sample of 50 cities and find that the average home cost in those cities is $294,706. We are interested in seeing if the cost of homes is increasing.

What is the standard error?

What is the margin of error at 90% confidence?

Using my sample of 50, what would be the 90% confidence interval for the population mean?

If I wanted to control my margin of error and set it to 20,000 at 90% confidence, what sample size would I need to take instead of the 50?

What are the null and alternative hypotheses?

What is the critical value at 90% confidence?

Calculate the test statistic (using the sample of 50 and NOT the answer from part d).

Find the p-value.

What conclusion would be made here at the 90% confidence level?

Answer 1

Solution:-

a) The standard error is 29547.87.

b) The margin of error at 90% confidence is 48606.25.

M.E = 1.645*29547.87

M.E = 48606.25

c) 90% confidence interval for the population mean is C.I = ( -246099.75 , 343312.25).

C.I = 294706 + 1.645*29547.87

C.I = 294706 + 48606.25

C.I = ( -246099.75 , 343312.25)

d) The required sample size would be 296.

n = 295.32

n = 296