In a manufacturing process the assembly line speed (feet per minute) was thought
ID: 3183402 • Letter: I
Question
In a manufacturing process the assembly line speed (feet per minute) was thought to affect the number of defective parts found during the inspection process. To test this theory, managers devised a situation in which the same batch of parts was inspected visually at variety of line speeds. They collected the following data.
Line Speed
Number of Defective Parts Found
20
21
20
19
40
15
30
16
60
14
40
17
a)Develop the estimated regression equation that relates line speed to the number of defective parts found.
b)At a 0.05 level of significance, determine whether line speed and number of defective parts found are related.
c)Did the estimated regression equation provide a good fit to the data? Explain.
d)Develop a 95% confidence interval to predict the mean number of defective parts for a line speed of 50 feet per minute.
Line Speed
Number of Defective Parts Found
20
21
20
19
40
15
30
16
60
14
40
17
Explanation / Answer
Answer:
a)Develop the estimated regression equation that relates line speed to the number of defective parts found.
Number of Defective Parts Found = 22.1739 - 0.1478*Line Speed
b)At a 0.05 level of significance, determine whether line speed and number of defective parts found are related.
Calculated F=11.33, P=0.0281 which is < 0.05 level.
line speed and number of defective parts found are related.
c)Did the estimated regression equation provide a good fit to the data? Explain.
R square =0.739. 73.9% of variance in Number of Defective Parts Found is explained by line speed.
The estimated regression equation provide a good fit to the data.
d)Develop a 95% confidence interval to predict the mean number of defective parts for a line speed of 50 feet per minute.
9%5 CI for predicted Number of Defective Parts Found when line speed is 50,
=(12.294, 17.271)
Regression Analysis
r²
0.739
n
6
r
-0.860
k
1
Std. Error
1.489
Dep. Var.
Number of Defective Parts Found
ANOVA table
Source
SS
df
MS
F
p-value
Regression
25.1304
1
25.1304
11.33
.0281
Residual
8.8696
4
2.2174
Total
34.0000
5
Regression output
confidence interval
variables
coefficients
std. error
t (df=4)
p-value
95% lower
95% upper
Intercept
22.1739
1.6527
13.416
.0002
17.5852
26.7627
Line Speed
-0.1478
0.0439
-3.367
.0281
-0.2697
-0.0259
Predicted values for: Number of Defective Parts Found
95% Confidence Interval
95% Prediction Interval
Line Speed
Predicted
lower
upper
lower
upper
Leverage
50
14.783
12.294
17.271
9.957
19.608
0.362
Regression Analysis
r²
0.739
n
6
r
-0.860
k
1
Std. Error
1.489
Dep. Var.
Number of Defective Parts Found
ANOVA table
Source
SS
df
MS
F
p-value
Regression
25.1304
1
25.1304
11.33
.0281
Residual
8.8696
4
2.2174
Total
34.0000
5
Regression output
confidence interval
variables
coefficients
std. error
t (df=4)
p-value
95% lower
95% upper
Intercept
22.1739
1.6527
13.416
.0002
17.5852
26.7627
Line Speed
-0.1478
0.0439
-3.367
.0281
-0.2697
-0.0259
Predicted values for: Number of Defective Parts Found
95% Confidence Interval
95% Prediction Interval
Line Speed
Predicted
lower
upper
lower
upper
Leverage
50
14.783
12.294
17.271
9.957
19.608
0.362
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