Question 6 (1 point) The mean area of homes in a certain city built in 2009 was

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Question 6 (1 point) 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 2,295 square feet, with a standard deviation of 225 square feet. An insurance company wants to know if the mean area of hom nTE in 2010 is less than that of homes built in 2009, Compute the P-value of the test. will need it for the next ques Write down your P-value. You Write only a number as your answer. Round to four decimal places (for example: 0.3841) Your Answer: Answer Save Question 7 (1 point) 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? O 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 O in 2009

Explanation / Answer

Question 6

Here, we have to use one sample t test for population mean.

H0: µ = 2438

Ha: µ < 2438

This is a left tailed or lower tailed test. This is a one tailed test.

Test statistic = t = (Xbar - µ) / [S/sqrt(n)]

We are given

Xbar = 2295

S = 225

n = 11

df = n – 1 = 11 – 1 = 10

Test statistic = t = (2295 – 2438) / [225/sqrt(11)

Test statistic = t = (2295 – 2438) /67.8401

Test statistic = t = -2.1079

P-value = 0.0306

(By using t-table or excel)

Question 7

We are given

= 0.05

We have

P-value = 0.0306

P-value < = 0.05

So, we reject the null hypothesis

There is evidence to conclude that the mean area of homes built in 2010 is less than that of homes built in 2009.

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