Question

The data for a sample showing the average and median housing prices for selected areas in a country in November 2007 and November 2008 is given in the accompanying table. Assume the data can be viewed as samples of the relevant populations. Complete parts a through d below.

November_2007_Average	November_2007_Median	November_2008_Average	November_2008_Median
356200	260900	229700	158500
329100	235900	226900	174200
308500	226300	242200	182800
291500	216400	243800	190700
281000	209000	244300	184000
285600	201000	243800	192000
263500	192800	238300	177800
256200	189000	_	_
246500	185000	_	_
238700	173500	_	_

a. Discuss whether the two samples are independent or dependent.

A. The samples are independent.

B. The data consists of both the average and median selling prices for the same houses. Knowing the median selling price would make it more likely that the mean selling price would be known. The samples are independent.

C. The data consists of both the average and median selling prices for the same houses. Knowing the median selling price would make it more likely that the mean selling price would be known. The samples are dependent.

D. There is insufficient information to determine if the samples are independent.

b. Based on your answer to part​ a, calculate a 90​% confidence interval for the difference between the means of the average and median selling prices for houses during November 2007.

​(______​,_______​) ​(Round to the nearest integer as​ needed.)

c. Noting your answer to part​ b, would it be plausible to assert that the mean of the average selling prices for houses during November 2007 is more than the average of the median selling prices during this​ period?

A. Since the confidence interval provides the range of plausible values for the difference and the confidence interval only contains positive​ numbers, this indicates that it is not plausible.

B. Since the confidence interval provides the range of plausible values for the difference and the confidence interval only contains positive​ numbers, this indicates that it is plausible.

C. Since the confidence interval provides the range of plausible values for the difference and the confidence interval only contains negative​ numbers, this indicates that it is plausible.

D. Since the confidence interval provides the range of plausible values for the difference and the confidence interval does not contain 50 comma 000 it is not plausible.

d. Using a​ p-value approach and a significance level of 0.10​, conduct a hypothesis test to determine if the mean of the average selling prices for houses during November 2007 is more than ​$50 comma 000 larger than the mean of the median selling prices during this period.

Let mudequalsmu1minusmu2​, where mu1 is the average selling price in November 2007 and mu2 is the median selling price in November 2007. Determine the null and alternative hypotheses. Choose the correct answer below.

A. Upper H 0​: mu Subscript dequals50,000

Upper H Subscript Upper A​: mu Subscript dnot equals50,000

B. Upper H 0​: mu Subscript dgreater than or equals0

Upper H Subscript Upper A​: mu Subscript dless than0

C. Upper H 0​: mu Subscript dnot equals0

Upper H Subscript Upper A​: mu Subscript dequals0

D. Upper H 0​: mu Subscript dless than or equals 50,000

Upper H Subscript Upper A​: mu Subscript dgreater than 50,000

Calculate the test statistic.

T= ______ ​(Round to two decimal places as​ needed.)

Calculate the​ p-value.

​p-value equals _______ ​(Round to three decimal places as​ needed.)

State the conclusion.

A.

Reject Upper H 0. There is insufficient evidence that the mean of the average selling prices for November 2007 is more than ​$50,000 larger than the mean of the median selling prices in November 2007.

B.

Do not reject Upper H 0. There is insufficient evidence that the mean of the average selling prices for November 2007 is more than ​$50,000 larger than the mean of the median selling prices in November 2007.

C.

Do not reject Upper H 0. There is sufficient evidence that the mean of the average selling prices for November 2007 is more than ​$50,000 larger than the mean of the median selling prices in November 2007.

D.

Reject Upper H 0. There is sufficient evidence that the mean of the average selling prices for November 2007 is more than ​$50,000 larger than the mean of the median selling prices in November 2007

Answer 1

a:

C. The data consists of both the average and median selling prices for the same houses. Knowing the median selling price would make it more likely that the mean selling price would be known. The samples are dependent.

b:

Here we have paired data. Following is the output of paired t test generated by excel:

Hence, required confidence interval is ($63499, $74854).

c:

B. Since the confidence interval provides the range of plausible values for the difference and the confidence interval only contains positive​ numbers, this indicates that it is plausible.

d:

For hypotheses, correct option is D.

The test statistics is:

t = 5.90

The p-value is:

p-value = 0.0000

Since p-value is less than 0.10 so we reject the null hypothesis.

Correct option:

D.

Reject Upper H 0. There is sufficient evidence that the mean of the average selling prices for November 2007 is more than ​$50,000 larger than the mean of the median selling prices in November 2007