Two machines are used to package laundry detergent. It is known that weights of boxes are normally distributed. Four boxes from each machine have their contents carefully weighed, with the following results (in grams):

An engineer wishes to test the null hypothesis that the mean weights of boxes from the two machines are equal. He decides to assume that the population variances are equal, reasoning as follows:

The sample variances are s²₁ = 7.00 for machine 1 and s²₂ = 17.33 for machine 2. The F statistic for testing for equality of population variances is F_3,3 = s²₂/s²₁= 2.48. The upper 10% point of the F_3,3distribution is 5.39. Since the null hypothesis specifies that the variances are equal, I determine that the P-value is greater than 2(0.10) = 0.20. Therefore I do not reject the null hypothesis, and I conclude that the variances are equal.

a. Has the F test been done correctly?

b. Is the conclusion justified? Explain.

Machine 1: 1752 1757 1751 1754 Machine 2: 1756 1750 1752 1746