Question

You may need to use the appropriate technology to answer this question.

Home values tend to increase over time under normal conditions, but the recession of 2008 and 2009 has reportedly caused the sales price of existing homes to fall nationwide.† You would like to see if the data support this conclusion. The file HomePrices contains data on 30 existing home sales in 2006 and 40 existing home sales in 2009.

2006 ($)

213,100	226,200	239,100
214,300	161,700	181,200
228,600	222,100	228,900
235,800	219,400	238,800
301,800	264,200	320,200
315,000	118,900	172,400
137,500	212,800	175,400
311,400	296,900	292,500
287,700	246,500	195,600
155,300	152,400	211,200

2009 ($)

155,400	189,800	200,800	280,400
213,200	181,100	117,400	130,000
170,000	149,600	146,200	54,400
213,800	186,000	182,100	180,000
215,700	164,200	95,300	239,500
207,200	188,200	169,400	185,600
177,000	178,000	161,200	249,200
146,400	99,800	246,700	173,500
138,100	112,200	137,500	147,900
179,000	116,200	197,500	164,200

(a)

Provide a point estimate of the difference (in dollars) between the population mean prices for the two years. (Use year 2006 − year 2009. Round your answer to the nearest dollar.)

$

(b)

Develop a 99% confidence interval estimate of the difference (in dollars) between the resale prices of houses in 2006 and 2009. (Use year 2006 − year 2009. Round your answers to the nearest dollar.)

$  to $

(c)

Would you feel justified in concluding that resale prices of existing homes have declined from 2006 to 2009? Why or why not?

To answer this question, we need to conduct a hypothesis test.

State the null and alternative hypotheses. (Let μ₁ = mean home price in 2006 and let μ₂ = mean home price in 2009.)

H₀:μ₁ − μ₂ > 0

H_a:μ₁ − μ₂ ≤ 0

H₀:μ₁ − μ₂ ≤ 0

H_a:μ₁ − μ₂ > 0

    

H₀:μ₁ − μ₂ ≠ 0

H_a:μ₁ − μ₂ = 0

H₀:μ₁ − μ₂ = 0

H_a:μ₁ − μ₂ ≠ 0

H₀:μ₁ − μ₂ ≤ 0

H_a:μ₁ − μ₂ = 0

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion. (Use α = 0.01)

Do not reject H₀. We can conclude that existing home prices have declined between 2006 and 2009.

Do not reject H₀. We can not conclude that existing home prices have declined between 2006 and 2009.  

Reject H₀. We can conclude that existing home prices have declined between 2006 and 2009

.Reject H₀. We can not conclude that existing home prices have declined between 2006 and 2009.

Answer 1

Following is the output of descriptive statistics generated by excel:

Descriptive statistics
	2006 ($)	2009 ($)
count	30	40
mean	2,25,896.67	1,70,992.50
sample standard deviation	55,207.36	44,958.26
sample variance	3,04,78,52,747.13	2,02,12,44,814.10
minimum	118900	54400
maximum	320200	280400
range	201300	226000

So we have

(a)

A point estimate of the difference (in dollars) between the population mean prices for the two years is

(b)

(c)

Conclusion:  Reject H₀. We can conclude that existing home prices have declined between 2006 and 2009