St. Paul, Minnesota home sample
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A sample of 12 homes sold last week in St. Paul, Minnesota, is selected. Can we conclude that as the size of the home (reported below in thousands of square feet) increases, the selling price (reported in $ thousands) also increases?
Home Size Selling
(thousands Price
of square feet) ($ thousands)
X Y X Y XY
1.4 100 1.96 10000 140
1.3 110 3.9 12100 143
1.2 105 1.44 11025 126
1.1 120 1.21 14400 132
1.4 80 1.96 6400 112
1.0 105 1 11025 105
1.3 110 3.9 12100 143
0.8 85 .64 7225 68
1.2 105 1.44 11025 126
0.9 75 .81 5625 67.5
1.1 70 1.21 4900 77
1.1 95 1.21 9025 104.5
Total 13.8 1160 20.68 114850 1344
a. Compute the coefficient of correlation.
b. Determine the coefficient of determination.
c. Can we conclude that there is a positive association between the size of the home and the selling price? Use the .05 significance level.
a. r = .087
b. r = (.087) = 0.0076
c. H : p 0; p>0. Reject H if t >
t = = .275
We cannot conclude that there is a positive correlation between the size of the home and the selling price.
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Solution Summary
The solution outlines:
A sample of 12 homes sold last week in St. Paul, Minnesota, is selected. Can we conclude that as the size of the home (reported below in thousands of square feet) increases, the selling price (reported in $ thousands) also increases?
Home Size Selling
(thousands Price
of square feet) ($ thousands)
X Y X Y XY
1.4 100 1.96 10000 140
1.3 110 3.9 12100 143
1.2 105 1.44 11025 126
1.1 120 1.21 14400 132
1.4 80 1.96 6400 112
1.0 105 1 11025 105
1.3 110 3.9 12100 143
0.8 85 .64 7225 68
1.2 105 1.44 11025 126
0.9 75 .81 5625 67.5
1.1 70 1.21 4900 77
1.1 95 1.21 9025 104.5
Total 13.8 1160 20.68 114850 1344
a. Compute the coefficient of correlation.
b. Determine the coefficient of determination.
c. Can we conclude that there is a positive association between the size of the home and the selling price? Use the .05 significance level.
a. r = .087
b. r = (.087) = 0.0076
c. H : p 0; p>0. Reject H if t >
t = = .275
We cannot conclude that there is a positive correlation between the size of the home and the selling price.
---
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
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