t tests state the meaning of μ first – solutions on page 629 (p value = .0569) p 345 9.74 a -e Use the TI-84 t test and the p value decision rule. Z test for the proportion State the meaning of P first - solutions on page 629 p 340 9.56 b Use the TI-84 one prop Z test and the p value decision rule, plus determine a (1-α)% CI for P CI for P: (.5608, .6392) Does the CI support the decision? 2 sample t test State µ1 and µ2 first and use the TI-84 2 sample t test and interval WiFi Tablet Battery life hours 4G Tablet Battery Life Hours x̄ 12.8333 8.1571 s 1.2623 4.606 n 12 7 Determine at the 5% level if there is evidence from the sample data that the mean battery life is significantly higher for the tablet with WiFi than the tablet with 4G. Plus calculate and completely interpret a (1-α)% CI for µWiFi - µ4G. Does the interval support the decision? If yes, then how many more hours does the battery last for the WiFi tablet? The pooled variance tSTAT = 3.3689 and the p value = .001822; the CI for µWiFi - µ4G is between (1.7477, 7.6047) lifetime hours. Chi Square Tests State the meaning of the P’s and the value of the ’s for the ‘difference in proportion Χ2 test’; and for ‘Χ2 test for independence’ state the meaning of the two categories; use the p value decision rule - solutions on page 663 p 443 11.32 b hint: there are 5 P’s p 440 11.24 the p value = 0.00 < 0.01… Simple Regression Analysis Solutions will be here after the due date… We want to develop a regression model to predict the assessed value of houses based on the heating area of houses in square feet. A sample of 15 single-family houses in the Kalamazoo area is selected. The assessed value in dollars and the heating area of the houses in square feet are recorded and stored in the data set House 3 (in the class Minitab Files folder). We are not using the Age in years column. House Assessed Value in $ Heating Area of house in sq ft Age in years 1 184400 2000 54 2 177400 1710 11.50 3 175700 1450 8.33 4 185900 1760 0.00 5 179100 1930 7.42 6 170400 1200 32 7 175800 1550 16 8 185900 1930 2 9 178500 1590 1.75 10 179200 1500 2.75 11 186700 1900 0.00 12 179300 1390 0.00 13 174500 1540 12.58 14 183800 1890 2.75 15 176800 1590 7.17 Interpret the meaning of the Y intercept; b0 and the slope b1 in the model. Predict the assessed value for a house whose heating area is 1,750 square feet. Determine the coefficient of determination, r2, and interpret its meaning. At the 0.05 level of significance, is there evidence of a significant linear relationship between assessed value and heating area? e) Determine the S.D. of ŷ. What units is it in? f) Construct a 95% CI for the slope B1 g) Determine a 95% interval estimate for the assessed value of a home with 1750 sq. ft. of heating area. h) What is the strength of the linear relationship between assessed value and heating area? Regression Analysis: Assessed Value versus Heating Area Source DF Adj SS Adj MS F-Value P-Value Regression 1 214374192 214374192 25.16 0.000 Heating Area 1 214374192 214374192 25.16 0.000 Error 13 110761808 8520139 Lack-of-Fit 11 86196808 7836073 0.64 0.748 Pure Error 2 24565000 12282500 Total 14 325136000 Model Summary S R-sq R-sq(adj) R-sq(pred) 2918.93 65.93% 63.31% 54.98% Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 151915 5563 27.31 0.000 Heating Area 16.63 3.32 5.02 0.000 1.00 Regression Equation Assessed Value = 151915 + 16.63 Heating Area Prediction Fit SE Fit 95% CI 95% PI 181024 808.185 (179278, 182770) (174481, 187567) Fit SE Fit 95% CI 95% PI 185182 1350.64 (182264, 188100) (178234, 192130)
t tests state the meaning of μ first – solutions on page 629 (p value = .0569)
p 345 9.74 a -e Use the TI-84 t test and the p value decision rule.
Z test for the proportion State the meaning of P first - solutions on page 629
p 340 9.56 b Use the TI-84 one prop Z test and the p value decision rule, plus determine a (1-α)% CI for P CI for P: (.5608, .6392)
Does the CI support the decision?
2 sample t test State µ1 and µ2 first and use the TI-84 2 sample t test and interval
|
|
WiFi Tablet Battery life hours |
4G Tablet Battery Life Hours |
|
x̄ |
12.8333 |
8.1571 |
|
s |
1.2623 |
4.606 |
|
n |
12 |
7 |
Determine at the 5% level if there is evidence from the sample data that the
Chi Square Tests State the meaning of the P’s and the value of the ’s for the ‘difference in proportion Χ2 test’; and for ‘Χ2 test for independence’ state the meaning of the two categories; use the p value decision rule - solutions on page 663
p 443 11.32 b hint: there are 5 P’s
p 440 11.24 the p value = 0.00 < 0.01…
Simple
We want to develop a regression model to predict the assessed value of houses based on the heating area of houses in square feet. A sample of 15 single-family houses in the Kalamazoo area is selected. The assessed value in dollars and the heating area of the houses in square feet are recorded and stored in the data set House 3 (in the class Minitab Files folder). We are not using the Age in years column.
|
House |
Assessed Value in $ |
Heating Area of house in sq ft |
Age in years |
|
1 |
184400 |
2000 |
54 |
|
2 |
177400 |
1710 |
11.50 |
|
3 |
175700 |
1450 |
8.33 |
|
4 |
185900 |
1760 |
0.00 |
|
5 |
179100 |
1930 |
7.42 |
|
6 |
170400 |
1200 |
32 |
|
7 |
175800 |
1550 |
16 |
|
8 |
185900 |
1930 |
2 |
|
9 |
178500 |
1590 |
1.75 |
|
10 |
179200 |
1500 |
2.75 |
|
11 |
186700 |
1900 |
0.00 |
|
12 |
179300 |
1390 |
0.00 |
|
13 |
174500 |
1540 |
12.58 |
|
14 |
183800 |
1890 |
2.75 |
|
15 |
176800 |
1590 |
7.17 |
- Interpret the meaning of the Y intercept; b0 and the slope b1 in the model.
- Predict the assessed value for a house whose heating area is 1,750 square feet.
- Determine the coefficient of determination, r2, and interpret its meaning.
- At the 0.05 level of significance, is there evidence of a significant linear relationship between assessed value and heating area?
- e) Determine the S.D. of ŷ. What units is it in?
- f) Construct a 95% CI for the slope B1
- g) Determine a 95%
interval estimate for the assessed value of a home with 1750 sq. ft. of heating area.
- h) What is the strength of the linear relationship between assessed value and heating area?
Regression Analysis: Assessed Value versus Heating Area
|
Source |
DF |
Adj SS |
Adj MS |
F-Value |
P-Value |
|
Regression |
1 |
214374192 |
214374192 |
25.16 |
0.000 |
|
Heating Area |
1 |
214374192 |
214374192 |
25.16 |
0.000 |
|
Error |
13 |
110761808 |
8520139 |
|
|
|
Lack-of-Fit |
11 |
86196808 |
7836073 |
0.64 |
0.748 |
|
Pure Error |
2 |
24565000 |
12282500 |
|
|
|
Total |
14 |
325136000 |
|
|
|
Model Summary
|
S |
R-sq |
R-sq(adj) |
R-sq(pred) |
|
2918.93 |
65.93% |
63.31% |
54.98% |
Coefficients
|
Term |
Coef |
SE Coef |
T-Value |
P-Value |
VIF |
|
Constant |
151915 |
5563 |
27.31 |
0.000 |
|
|
Heating Area |
16.63 |
3.32 |
5.02 |
0.000 |
1.00 |
Regression Equation
|
Assessed Value |
= |
151915 + 16.63 Heating Area |
|
|
|
|
Prediction
|
Fit |
SE Fit |
95% CI |
95% PI |
|
181024 |
808.185 |
(179278, 182770) |
(174481, 187567) |
|
Fit |
SE Fit |
95% CI |
95% PI |
|
185182 |
1350.64 |
(182264, 188100) |
(178234, 192130) |
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