The variance in a production process is an important measure of the quality of t

Question

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. A statistical test was performed in Excel to determine whether there is a significant difference between the variances in the bag weights for two machines. Answer the following questions according to the provided output. 1. If the null hypothesis H_0: sigma^2_1 = sigma^2_2 is tested at the 5% level, can we reject H_0? a. Yes, because our one-tailed p-value (.00000361079) is smaller than the given alpha/2 of .025 b. Yes, because our one-tailed p-value (.00000361079) is smaller than the given alpha of .05 c. Yes, because our F stat (8.28) is greater than the one-tail F critical value of 2.05 d. Yes, because our F stat (8.28) is greater than 2 times 2.05 (double of the one-tail F critical value) At the .05 level of significance, if the null hypothesis of H_0: sigma^2_1 = sigma^2_2 is rejected, it can be concluded that a. the variances in the bag weights both machines are not significantly different b. the variances in the bag weights for two machines are significantly different c. the variance in the bag weights for Machine 1 is significantly greater than that of Machine 2 d. the variance in the bag weights for Machine 2 is significantly greater than that of Machine 1

Explanation / Answer

Q1 option c) yes because our F stat(8.28) is greater than one tailed F critical value of 2.05

Q2 option a) the variance in the bag weighs both machines are not significantly different.

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