At the 1% significance level, can you conclude that the mean number of calories per scoop are different for these two brands of performance feed?

Question

 A sample of 14 scoops of Brand I performance feed gave the mean number of calories of 156 per scoop  with a standard deviation of 38 calories. Another sample of 18 cans of Brand II performance feed gave the mean number of calories of 144 with a standard deviation of 40 calories. At the 1% significance level, can you conclude that the mean number of calories per scoop are different for these two brands of performance feed? Assume that the calories per scoop are normally distributed for each of the two brands and that the standard deviations for the two populations are equal.

Answer 1

If you assume equal variances of the two brands, you can use the pooled 2-sampled t-test

The approximation for the pooled variance, S_p² = ((n₁-1)s₁²+(n₂-1)s₂²)/(n₁+n₂-2) = (13*38+17*40)/(13+17) = 39.13

Now t statistic for the difference in means is defined as (X₁-X₂)/S_Psqrt(1/n₁+1/n₂) = (156-144)/(sqrt(39.13)sqrt(1/18+1/14)) = 5.38

Compare this statistic with t₃₀(P = .5%) as this is two-sided test (Clearly different)