The accompanying data in the table below were derived from life tests for two di
ID: 3045592 • Letter: T
Question
The accompanying data in the table below were derived from life tests for two different brands of cutting tools. Complete parts a through c.
Cutting Speed in meters Brand A (Useful life in hours) Brand B (Useful life in hours)
30 4.3 5.5
30 4.4 6.9
30 4.9 4.7
40 5.1 5.5
40 3.7 4.8
40 2.5 5.0
50 4.4 4.5
50 2.8 4.0
50 1.0 3.7
60 4.0 3.8
60 2.0 3.0
60 1.1 2.4
70 1.1 1.5
70 0.5 2.0
70 3.0 1.0
a. Use a 90% 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.
The mean useful life of a brand A cutting tool when the cutting speed is 45 meters per minute is ____ to ____hours. (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 ____to ______hours. (Round to one decimal place as needed.)
b. Use a 90% prediction interval to predict 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.
The predicted useful life of a brand A cutting tool when the cutting speed is 45 meters per minute is ____ to___ hours. (Round to one decimal place as needed.)
The predicted useful life of a brand B cutting tool when the cutting speed is 45 meters per minute is ___ to ____ hours. (Round to one decimal place as needed.
c. Supposed you were asked to predict the useful life of brand A cutting tool with a cutting speed of x=100 meters per minute. Because the given value of x is given outside the range of the sample x-values, the prediction is an example of an extrapolation. Predict the useful life of brand A cutting tool that is 100 meters per minute and construct a 90% prediction interval for the actual useful life of the tool.
The predicted useful life of brand A cutting tool that is operated at 100 meters per minute is ___ hours. (Round to two decimal places as needed)
The actual useful life of brand A cutting tool when the speed is 100 meters per minute is ___ to ____hours. (Round to two decimal places as needed)
Explanation / Answer
Answer:
a. Use a 90% 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.
The mean useful life of a brand A cutting tool when the cutting speed is 45 meters per minute is 2.8 to 3.9 hours. (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 4.1 to 4.7 hours. (Round to one decimal place as needed.)
b. Use a 90% prediction interval to predict 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.
The predicted useful life of a brand A cutting tool when the cutting speed is 45 meters per minute is 1.2 to 5.5 hours. (Round to one decimal place as needed.)
The predicted useful life of a brand B cutting tool when the cutting speed is 45 meters per minute is 3.2 to 5.6 hours. (Round to one decimal place as needed.
c. Supposed you were asked to predict the useful life of brand A cutting tool with a cutting speed of x=100 meters per minute. Because the given value of x is given outside the range of the sample x-values, the prediction is an example of an extrapolation. Predict the useful life of brand A cutting tool that is 100 meters per minute and construct a 90% prediction interval for the actual useful life of the tool.
The predicted useful life of brand A cutting tool that is operated at 100 meters per minute is -0.71 hours. (Round to two decimal places as needed)
The actual useful life of brand A cutting tool when the speed is 100 meters per minute is -3.5 to 2.1 hours. (Round to two decimal places as needed)
Regression Analysis
r²
0.485
n
15
r
-0.696
k
1
Std. Error
1.159
Dep. Var.
Brand A
ANOVA table
Source
SS
df
MS
F
p-value
Regression
16.4280
1
16.4280
12.24
.0039
Residual
17.4493
13
1.3423
Total
33.8773
14
Regression output
confidence interval
variables
coefficients
std. error
t (df=13)
p-value
90% lower
90% upper
Intercept
6.6867
1.0991
6.084
3.88E-05
4.7402
8.6331
speed
-0.0740
0.0212
-3.498
.0039
-0.1115
-0.0365
Predicted values for: Brand A
90% Confidence Intervals
90% Prediction Intervals
speed
Predicted
lower
upper
lower
upper
Leverage
45
3.3567
2.7948
3.9186
1.2294
5.4839
0.075
100
-0.7133
-2.6598
1.2331
-3.5414
2.1148
0.900
Regression Analysis
r²
0.859
n
15
r
-0.927
k
1
Std. Error
0.643
Dep. Var.
Brand B
ANOVA table
Source
SS
df
MS
F
p-value
Regression
32.6563
1
32.6563
78.89
6.99E-07
Residual
5.3810
13
0.4139
Total
38.0373
14
Regression output
confidence interval
variables
coefficients
std. error
t (df=13)
p-value
90% lower
90% upper
Intercept
9.1033
0.6104
14.915
1.48E-09
8.0224
10.1842
speed
-0.1043
0.0117
-8.882
6.99E-07
-0.1251
-0.0835
Predicted values for: Brand B
90% Confidence Intervals
90% Prediction Intervals
speed
Predicted
lower
upper
lower
upper
Leverage
45
4.4083
4.0963
4.7204
3.2270
5.5896
0.075
100
-1.3300
-2.4109
-0.2491
-2.9005
0.2405
0.900
Regression Analysis
r²
0.485
n
15
r
-0.696
k
1
Std. Error
1.159
Dep. Var.
Brand A
ANOVA table
Source
SS
df
MS
F
p-value
Regression
16.4280
1
16.4280
12.24
.0039
Residual
17.4493
13
1.3423
Total
33.8773
14
Regression output
confidence interval
variables
coefficients
std. error
t (df=13)
p-value
90% lower
90% upper
Intercept
6.6867
1.0991
6.084
3.88E-05
4.7402
8.6331
speed
-0.0740
0.0212
-3.498
.0039
-0.1115
-0.0365
Predicted values for: Brand A
90% Confidence Intervals
90% Prediction Intervals
speed
Predicted
lower
upper
lower
upper
Leverage
45
3.3567
2.7948
3.9186
1.2294
5.4839
0.075
100
-0.7133
-2.6598
1.2331
-3.5414
2.1148
0.900
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.