Two methods of filling boxes of cereal produce the same package fill weight on the average.The second method is faster, but some people suspect that this method produces a greater variance in fill amounts than the first method does.A random sample of 31 packages filled by method 1 is obtained, and the sample variance is S₁² = .6.A random sample of 25 packages filled by method 2 yields a sample variance S₂² = .4.

(5)(a) Let = .01Test H₀: . Use a one - tailed test.

(5)(b) Construct a 98% confidence interval for .