Question

Open House_Price data.

Test if there is a significant difference in house prices for houses that are less than 31 years old compared to houses that are 31 years or older. Answer the questions for Assessment. (Pick the closest answer)

1. What is the P-value?

• a. 0.106390147
• b. ​​1.85525E-07
• c. ​​0.002738669
• d. ​​0.000144083

2. What is the Statistical interpretation?

• a. The P-value is too small to have a conclusive answer.
• b. The P-value is much smaller than 5% thus we are very certain that house prices are different.
• c. ​​The P-value is larger than 5% thus the answer is inconclusive.
• d. The P-value is larger than 5% thus we are certain that house prices are not different.

3. What is the conclusion?

• a. Statistical interpretation agrees with the intuition: the house price is different due to the age of the house.
• b. ​​The statistics does not conform to the intuition since one would expect the house price to be different due to the age of the house.
• c. Since the test is inconclusive the conclusion is inconclusive as well.
• d. The test does not make statistical sense.

DATA: 
Age     #Bathrooms      #Rooms  #BedRooms       #FirePlaces     sellingPrice in $100000
42      1       7       4       0       4.9176
62      1       7       4       0       5.0208
40      1       6       3       0       4.5429
54      1       6       3       0       4.5573
42      1       6       3       0       5.0597
56      1       6       3       0       3.891
51      1       7       3       1       5.898
32      1       6       3       0       5.6039
32      1       6       3       0       5.8282
30      1       6       3       0       5.3003
30      1       5       2       0       6.2712
32      1       6       3       0       5.9592
32      1       6       3       0       5.6039
50      1.5     8       4       0       8.2464
17      1.5     6       3       0       7.7841
23      1       7       3       0       9.0384
22      1.5     6       3       0       7.5422
44      1.5     6       3       0       6.0931
3       1       7       3       0       8.14
31      1.5     8       4       0       9.1416
42      2.5     10      5       1       16.4202
14      2.5     9       5       1       14.4598
46      1       5       2       1       5.05
22      1.5     7       3       1       6.6969
40      1       6       3       1       5.9894
50      1.5     8       4       1       8.7951
48      1.5     8       4       1       8.3607
30      1.5     6       3       1       12

Answer 1

Age	sellingPrice
3	8.14
14	14.4598
17	7.7841
22	7.5422
22	6.6969
23	9.0384
30	5.3003
30	6.2712
30	12
31	9.1416
32	5.6039
32	5.8282
32	5.9592
32	5.6039
40	4.5429
40	5.9894
42	4.9176
42	5.0597
42	16.4202
44	6.0931
46	5.05
48	8.3607
50	8.2464
50	8.7951
51	5.898
54	4.5573
56	3.891
62	5.0208

Two-Sample T-Test and CI: sellingPrice less than 31 ... r 31 years old

Method

μ₁: mean of sellingPrice less than 31 years

µ₂: mean of sellingPrice for 31 years and older

Difference: μ₁ - µ₂

Equal variances are not assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
sellingPrice less than 31 years	9	8.58	2.92	0.97
sellingPrice for 31 years and older	19	6.58	2.82	0.65

Estimation for Difference

Difference	95% CI for Difference
2.00	(-0.49, 4.49)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
1.72	15	0.1068418

1)

the P-value is 0.106390147

2) The P-value is larger than 5% thus we are certain that house prices are not different.

3) ​​The statistics does not conform to the intuition since one would expect the house price to be different due to the age of the house.