In a factory, two machines are used for filling plastic bottles with a net volume of 16.0 ounces. An investigation on the net volume was done. A random sample of 17 bottles produced by Machine 1 is taken while a random sample of 20 bottles produced by Machine 2 is taken, their net volumes were measured and recorded.

(a) Test the hypothesis that the net volumes of the bottles produced by these two machines have the same variances at a 5% significance level.

Machine 1 Machine 2 t-Test: Two-Sample Assuming Equal Variances t-Test: Two-Sample Assuming Unequal Variances 16.03 16.01 16.04 15.96 Machine 1 Machine 2 Machine 1 Machine 2 15.98 16.05 Mean 15.9936 15.9504 Mean 15.9936 15.9504 16.02 16.02 Variance 0.002340667 0.031795667 Variance 0.002340667 0.031795667 16.03 15.65 Observations 25 25 Observations 25 25 15.97 16.08 Pooled Variance 0.017068167 Hypothesized Mean Difference 0 15.96 15.48 Hypothesized Mean D 0 df 28 16.04 16.01 df 48 t Stat 1.169082921 15.95 16.04 t Stat 1.169082921 P(T