Question

The mean area of homes in a certain city built in 2009 was 2438 square feet. Assume that a simple random sample of 11 homes in the same city built in 2010 had a mean area of 2,297 square feet, with a standard deviation of 225 square feet. An insurance company wants to know if the mean area of homes built in 2010 is less than that of homes built in 2009. Compute the P-value of the test.

Write down your P-value. You will need it for the next question.

Write only a number as your answer. Round to four decimal places (for example: 0.3841).

In the last question, an insurance company wants to know if the mean area of homes built in 2010 is less than that of homes built in 2009. What is the conclusion at the 0.05 level of significance?

Question 13 options:

	There is evidence to conclude that the mean area of homes built in 2010 is less than that of homes built in 2009
	There is not enough evidence to conclude that the mean area of homes built in 2010 is less than that of homes built in 2009
	There is evidence to conclude that the mean area of homes built in 2010 is not less than that of homes built in 2009
	There is not enough evidence to conclude that the mean area of homes built in 2010 is not less than that of homes built in 2009

Answer 1

H0: = 2438

Ha: < 2438

Test statistics

t = - / S / sqrt(n)

= 2297 - 2438 / 225 / sqrt(11)

= -2.08

This is test statistics value.

Using T table,

p-value for one tailed test with t = 2.08 and df = 10

p-value = 0.0321

Conclusion -

Since p-value < 0.05, we have sufficient evidence to reject H0.

We conclude that ,

There is evidence to conclude that the mean are of the homes build in 2010 is less than that of homes

build in 2009.