The article "Evaluating Variability in Filling Operations" (Food Tech., 1984: 51-55) describes two different filling operations used in a ground-beef packing plant. Both filling operations were set to fill packages with 1400 g of ground beef. In a random sample of size 30 taken from each filling operation, the resulting means and standard deviations were 1402.24 g and 10.97 g for operation 1 and 1419.63 g and 9.96 g for operation 2.
a. Using a .05 significance level, is there sufficient evidence to indicate that the true mean weight of the packages differs for the two operations?
b. Does the data from operation 1 suggest that the true mean weight of packages produced by operation 1 is higher than 1400 g? Use a .05 significance level.