I have created my chart but am really confused on creating a Hypothesis and how to actually use the information obtained by my chart. The question is about the variance in a production process is an important measure of quality. A lrg var often signals an opportunity for improvement in the process of finding ways to reduce the process variance. Conduct stat test to determine whether there is a significant diff between variances in bag weights of two machines. Use .05 level of sig. What is conclusion? Which machine, if either, provides greater opportunity for improvement?

Question

I have created my chart but am really confused on creating a Hypothesis and how to actually use the information obtained by my chart. The question is about the variance in a production process is an important measure of quality. A lrg var often signals an opportunity for improvement in the process of finding ways to reduce the process variance. Conduct stat test to determine whether there is a significant diff between variances in bag weights of two machines. Use .05 level of sig. What is conclusion? Which machine, if either, provides greater opportunity for improvement?

Here is my chart

Machine I Machine II
Mean 3.3284 3.2782
Variance 0.0489 0.0059
Observations 25 22
df 24 21
F 8.2844
P(F<=f) one-tail 0.000004
F Critical one-tail 2.0540

I am at a loss as to how to interpret the information to answer the question. Thank You

Answer 1

To conduct a statistical test to determine whether there is a significant difference between the variances in bag weights of Machine I and Machine II, you can use the F-test for comparing variances.

First, let's break down the information in your chart:

- Machine I:
- Mean: 3.3284
- Variance: 0.0489
- Observations: 25
- Degrees of Freedom (df): 24

- Machine II:
- Mean: 3.2782
- Variance: 0.0059
- Observations: 22
- Degrees of Freedom (df): 21

Now, let's proceed with the hypothesis testing:

Step 1: State the null and alternative hypotheses:
- Null hypothesis (H0): There is no significant difference between the variances of bag weights for Machine I and Machine II.
- Alternative hypothesis (Ha): There is a significant difference between the variances of bag weights for Machine I and Machine II.

Step 2: Determine the significance level: In this case, it is given that the significance level (alpha) is 0.05.

Step 3: Calculate the test statistic and critical value:
- The test statistic (F) is given in your chart as 8.2844.
- The critical value of F at the alpha level of 0.05 (one-tail test) with 24 and 21 degrees of freedom is 2.0540.

Step 4: Compare the test statistic and critical value:
- If the test statistic (F) is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

In your case, the test statistic (F) is 8.2844, which is greater than the critical value of 2.0540.

Step 5: State the conclusion:
- Since the test statistic is greater than the critical value, we reject the null hypothesis. Therefore, we can conclude that there is a significant difference between the variances of bag weights for Machine I and Machine II.

Step 6: Determine which machine provides the greater opportunity for improvement:
- In this case, since Machine I has a larger variance (0.0489) compared to Machine II (0.0059), Machine I provides a greater opportunity for improvement in reducing the process variance.

In summary, the conclusion is that there is a significant difference between the variances of bag weights for Machine I and Machine II. Machine I provides a greater opportunity for improvement in reducing the process variance.