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. Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for the two machines. Use a level of significance. What is your conclusion? Which machine, if either, provides the greater opportunity for quality improvements? Click on the datafile logo to reference the data. (to 4 decimals) (to 4 decimals) (to 2 decimals) - Select your answer -

There is a sufficient evidence to support the that machine 1 has the greater variance.

Step-by-step explanation:

The question with the complete details can be found online.

Start by stating the hypotheses.

The null hypothesis states that the variance of machine 1 is less than or equal to machine 2

So, we have:

The alternate hypothesis will then be:

So, we have:

Calculate the mean of Machine 1 and 2

The mean is:

For machine 1, we have:

For machine 2, we have:

Calculate the standard deviation of both machines

The standard deviation is:

For machine 1, we have:

For machine 2, we have:

Calculate the degrees of freedom

For machine 1;

For machine 2

Calculate the test statistic (t)

Rewrite in terms of standard deviation

Lastly, calculate the p value.

This is the value of P(t > 8.2881) between the degrees of freedom i.e. 21 and 24

From the f distribution table

Hence, we reject the null hypothesis