Question

Homes for Sale

The dataset HomesForSale has data on houses available for sale in three Mid-Atlantic states (NY, NJ, and PA). Table 1 shows the mean and standard deviation from the three Mid-Atlantic states, in thousands of dollars. Use this table, the knowledge that within the US the average house sells for about 265 thousand dollars¹, and a 5% significance level to answer the following questions.

State	n	Mean	Std. Dev.
New York	30	565.6	697.6
New Jersey	30	388.5	224.7
Pennsylvania	30	249.6	179.3

Table 1 Mean housing prices for New York, New Jersey, and Pennsylvania


Click here for the dataset associated with this question.


¹According to the US Census in April 2011.

(a) Test whether the average cost of a house in New York is significantly greater than the US average.

Give the test statistic and the p-value.

Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.

test statistic = Enter your answer in accordance to item (a) of the question statement

p-value = Enter your answer in accordance to item (a) of the question statement

Is the average cost of a house in New York significantly greater than the US average?

(b) Test whether the average cost of a house in New Jersey is significantly greater than the US average.

Give the test statistic and the p-value.

Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.

test statistic = Enter your answer in accordance to item (b) of the question statement

p-value = Enter your answer in accordance to item (b) of the question statement

Is the average cost of a house in New Jersey significantly greater than the US average?

Choose the answer from the menu in accordance to item (b) of the question statement                                                                      YesNo

(c) Test whether the average cost of a house in Pennsylvania is significantly greater than the US average.

Give the test statistic and the p-value.

Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.

test statistic = Enter your answer in accordance to item (c) of the question statement

p-value = Enter your answer in accordance to item (c) of the question statement

Is the average cost of a house in Pennsylvania significantly greater than the US average?

Choose the answer from the menu in accordance to item (c) of the question statement                                                                      YesNo

(d) Which state shows the most evidence that the state average is greater than the US average?

New York

New Jersey

Pennsylvania

Answer 1

a)One-Sample T

Descriptive Statistics

N	Mean	StDev	SE Mean
30	565.6	697.6	127

μ: mean of House price in Newyork

Test

Null hypothesis	H₀: μ = 265
Alternative hypothesis	H₁: μ > 265

T-Value	P-Value
2.36	0.013

Since p-value is less than alpha 0.05, we reject null hypothesis and there is a significant evidence to conclude that the average cost of a house in New York significantly greater than the US average .

b)

One-Sample T

Descriptive Statistics

N	Mean	StDev	SE Mean
30	388.5	224.7	41.0

μ: mean of House price in New jersey

Test

Null hypothesis	H₀: μ = 265
Alternative hypothesis	H₁: μ > 265

T-Value	P-Value
3.01	0.003

Since p-value 0.003 is less than alpha 0.05, we reject null hypothesis and there is a significant evidence to conclude that the average cost of a house in New Jersey is significantly greater than the US average .

c)

One-Sample T

Descriptive Statistics

N	Mean	StDev	SE Mean
30	249.6	179.3	32.7

μ: mean of House price in Pennsylvania

Test

Null hypothesis	H₀: μ = 265
Alternative hypothesis	H₁: μ > 265

T-Value	P-Value
-0.47	0.679

Since p-value 0.679 is greater than alpha 0.05, we fail to reject null hypothesis and there is no significant evidence to conclude that the average cost of a house in New Jersey is significantly greater than the US average .

d) New Jersey state shows the most evidence that the state average is greater than the US average. Because its p-value is lesser than the others.