The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Machine 1 Machine 2 2.95 3.45 3.50 3.75 3.48 3.26 3.33 3.20 3.22 3.30 3.34 3.28 3.29 3.25 3.30 | 3.26 3.16 3.20 3.22| 3.38 | 3.90 3.36 3.25 3.28 3.38 3.34 3.35 3.19 3.35 3.05 3.36 3.28 3.20 3.22 2.98 3.45 3.70 3.34 3.18 3.35 3.30 3.28 3.30 3.20 3.16 3.33 3.12 Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for two machines. Use a 0.05 level of significance. What is your conclusion? State the null and alternative hypotheses. Hoi o,? > a,? Hoio,? = 02
The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Machine 1 Machine 2 2.95 3.45 3.50 3.75 3.48 3.26 3.33 3.20 3.22 3.30 3.34 3.28 3.29 3.25 3.30 | 3.26 3.16 3.20 3.22| 3.38 | 3.90 3.36 3.25 3.28 3.38 3.34 3.35 3.19 3.35 3.05 3.36 3.28 3.20 3.22 2.98 3.45 3.70 3.34 3.18 3.35 3.30 3.28 3.30 3.20 3.16 3.33 3.12 Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for two machines. Use a 0.05 level of significance. What is your conclusion? State the null and alternative hypotheses. Hoi o,? > a,? Hoio,? = 02
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Transcribed Image Text:Which machine, if either, provides the greater opportunity for quality improvements?
Machine 1 offers the best opportunity for process quality improvements.
Machine 2 offers the best opportunity for process quality improvements.
Neither machine offers an opportunity for process quality improvements.
Transcribed Image Text:The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the
process variance.
Machine 1
Machine 2
2.95
3.45
3.50
3.75
3.48
3.26
3.33
3.20
3.22
3.30
3.34
3.28
3.29
3.25
3.30
3.26
3.16
3.20
3.22
3.38
3.90
3.36
3.25
3.28
3.38
3.34
3.35
3.19
3.35
3.05
3.36
3.28
3.20
3.22
2.98
3.45
3.70
3.34
3.18
3.35
3.30
3.28
3.30
3.20
3.16
3.33
3.12
Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for two machines. Use a 0.05 level of significance. What is your conclusion?
State the null and alternative hypotheses.
2
Ho: 01 < 02
Ha: 01
2
02
2
2
> 02
2
2
2
2
Ho: 01
02
Ha: 01
= 02
2
Ho: 01
02
Ha: 01
+ 02
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value
State your conclusion.
Do not reject Ho. We can conclude that the process variances are significantly different.
0'
Reject Ho. We can conclude that the process variances are significantly different.
Do not reject Ho. We cannot conclude that the process variances are significantly different.
Reject Ho. We cannot conclude that the process variances are significantly different.
O O
Expert Solution
Step 1: Given:
Level of significance = = 0.05
Given data is,
| Machine 1 | Machine 2 |
| 2.95 | 3.22 |
| 3.45 | 3.3 |
| 3.5 | 3.34 |
| 3.75 | 3.28 |
| 3.48 | 3.29 |
| 3.26 | 3.25 |
| 3.33 | 3.3 |
| 3.2 | 3.26 |
| 3.16 | 3.38 |
| 3.2 | 3.3 |
| 3.22 | 3.35 |
| 3.38 | 3.19 |
| 3.9 | 3.35 |
| 3.36 | 3.05 |
| 3.25 | 3.36 |
| 3.28 | 3.28 |
| 3.2 | 3.3 |
| 3.2 | 3.28 |
| 2.98 | 3.3 |
| 3.45 | 3.2 |
| 3.7 | 3.16 |
| 3.34 | 3.33 |
| 3.18 | |
| 3.35 | |
| 3.12 |
We have to conduct a statistical test to determine whether there is significant difference between the variances in the bag weights of two machines.
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