To conduct a statistical test for comparing the variances of the bag weights for the two machines, we can use the F-test. The F-test compares the ratio of the variances of two populations.
Given the data, we need to calculate the variances for each machine and then the F-statistic to compare the variances. The formulas are as follows:
Variance = (sum of (x - mean)^2) / (n - 1)
F-statistic = variance of machine 1 / variance of machine 2
Let's calculate the variances and F-statistic using the provided sample data.
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. Jelly Belly Candy Company is testing two machines that use different technologies to fill three pound bags of jelly beans. The file Bags contains a sample of data on the weights of bags (in pounds) filled by each machine. 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 0.05 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. DATA variance machine 1= variance machine 2= F=(to 4 decimals) (to 2 decimals) (to 4 decimals)
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