Cutting Speed (meters per minute) Useful Life Brand A (Hours) Useful Life Brand
ID: 3313871 • Letter: C
Question
Cutting Speed (meters per minute)
Useful Life Brand A (Hours)
Useful Life Brand B (Hours)
30
5.7
5.6
30
3.6
6.9
30
5.4
5.3
40
5.1
6.5
40
3.6
4.1
40
2.5
5
50
4.4
4.5
50
2.8
4
50
1
3.7
60
4
3.8
60
2
3
60
1.1
2.4
70
1.1
1.5
70
0.5
2
70
3
1
Use a 95 % confidence interval to estimate the mean useful life of a brand A cutting tool when the cutting speed is 45
meters per minute. Repeat for brand B. Compare the widths of the two intervals and comment on the reasons for any difference.
c. Suppose you were asked to predict the useful life of a brand A cutting tool for a cutting speed of
x=100
meters per minute. Because the given value of x is outside the range of the sample x-values, the prediction is an example of extrapolation. Predict the useful life of a brand A cutting tool that is operated at
100 meters per minute and construct a 95% prediction interval for the actual useful life of the tool. What additional assumption do you have to make in order to ensure the validity of an extrapolation? The predicted useful life of a brand A cutting tool that is operated at
100meters per minute is (Round to two decimal places as needed.)
The actual predicted useful life of a brand A cutting tool when the speed is
100meters per minute is (Round to one decimal place as needed.)
The mean useful life of a brand A cutting tool when the cutting speed is 45 meters per minute is
(Round to one decimal place as needed.)
The mean useful life of a brand B cutting tool when the cutting speed is 45 meters per minute is
(Round to one decimal place as needed.)
b. Use a 95 % prediction interval to predict the useful life of a brand A cutting tool when the cutting speed is 45 meters per minute. Repeat for brand B.
The predicted useful life of a brand A cutting tool when the speed is 45 meters per minute is
(Round to one decimal place as needed.)
The predicted useful life of a brand B cutting tool when the speed is 45 meters per minute is
(Round to one decimal place as needed.)
Cutting Speed (meters per minute)
Useful Life Brand A (Hours)
Useful Life Brand B (Hours)
30
5.7
5.6
30
3.6
6.9
30
5.4
5.3
40
5.1
6.5
40
3.6
4.1
40
2.5
5
50
4.4
4.5
50
2.8
4
50
1
3.7
60
4
3.8
60
2
3
60
1.1
2.4
70
1.1
1.5
70
0.5
2
70
3
1
Explanation / Answer
Result:
Use a 95 % confidence interval to estimate the mean useful life of a brand A cutting tool when the cutting speed is 45meters per minute.
Regression Analysis
r²
0.444
n
15
r
-0.666
k
1
Std. Error
1.139
Dep. Var.
A
ANOVA table
Source
SS
df
MS
F
p-value
Regression
13.4670
1
13.4670
10.39
.0067
Residual
16.8530
13
1.2964
Total
30.3200
14
Regression output
confidence interval
variables
coefficients
std. error
t (df=13)
p-value
95% lower
95% upper
Intercept
6.2500
1.0802
5.786
.0001
3.9165
8.5835
speed
-0.0670
0.0208
-3.223
.0067
-0.1119
-0.0221
Predicted values for: A
95% Confidence Interval
95% Prediction Interval
speed
Predicted
lower
upper
lower
upper
Leverage
45
3.2350
2.5614
3.9086
0.6847
5.7853
0.075
The regression equation for A,
Speed = 6.25-0.067*A
95% confidence interval when A=45, (2.5614, 3.9086).
Repeat for brand B. Compare the widths of the two intervals and comment on the reasons for any difference.
Regression Analysis
r²
0.849
n
15
r
-0.921
k
1
Std. Error
0.680
Dep. Var.
B
ANOVA table
Source
SS
df
MS
F
p-value
Regression
33.7080
1
33.7080
72.84
1.09E-06
Residual
6.0160
13
0.4628
Total
39.7240
14
Regression output
confidence interval
variables
coefficients
std. error
t (df=13)
p-value
95% lower
95% upper
Intercept
9.1800
0.6454
14.225
2.65E-09
7.7858
10.5742
speed
-0.1060
0.0124
-8.535
1.09E-06
-0.1328
-0.0792
Predicted values for: B
95% Confidence Interval
95% Prediction Interval
speed
Predicted
lower
upper
lower
upper
Leverage
45
4.4100
4.0075
4.8125
2.8862
5.9338
0.075
The regression equation for B,
Speed = 9.18-0.106*B
95% confidence interval when B=45, (4.0075,4.8125 ).
c. Suppose you were asked to predict the useful life of a brand A cutting tool for a cutting speed of
x=100meters per minute. Because the given value of x is outside the range of the sample x-values, the prediction is an example of extrapolation.
The mean useful life of a brand A cutting tool when the cutting speed is 45 meters per minute is
(Round to one decimal place as needed.) 3.2
The mean useful life of a brand B cutting tool when the cutting speed is 45 meters per minute is
(Round to one decimal place as needed.) 4.4
b. Use a 95 % prediction interval to predict the useful life of a brand A cutting tool when the cutting speed is 45 meters per minute. Repeat for brand B.
The predicted useful life of a brand A cutting tool when the speed is 45 meters per minute is
(Round to one decimal place as needed.) (0.7, 5.8)
The predicted useful life of a brand B cutting tool when the speed is 45 meters per minute is
(Round to one decimal place as needed.) (2.9, 5.9)
Regression Analysis
r²
0.444
n
15
r
-0.666
k
1
Std. Error
1.139
Dep. Var.
A
ANOVA table
Source
SS
df
MS
F
p-value
Regression
13.4670
1
13.4670
10.39
.0067
Residual
16.8530
13
1.2964
Total
30.3200
14
Regression output
confidence interval
variables
coefficients
std. error
t (df=13)
p-value
95% lower
95% upper
Intercept
6.2500
1.0802
5.786
.0001
3.9165
8.5835
speed
-0.0670
0.0208
-3.223
.0067
-0.1119
-0.0221
Predicted values for: A
95% Confidence Interval
95% Prediction Interval
speed
Predicted
lower
upper
lower
upper
Leverage
45
3.2350
2.5614
3.9086
0.6847
5.7853
0.075
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