Question

A national food processor is studying two meat additives to determine if they differ on the mean amount of time (in hours) that it takes for the meat to spoil. They are particularly interested in how effective the additive is on ribeye steaks. Suppose 16 ribeye cuts are treated with additive A and 16 are treated with additive B. The results are summarized in the table below: Mean Standard Deviation Additive 1 (Group 1) 108.1 10.6 Additive B (Group 2) 125 7 Compute the test statistic to test the hypothesis at the 0.01 level of significance that the two means differ under the assumption of unequal population standard deviations (Case 2). Take all calculations to three decimal places.

Answer 1

If unequal population standard deviations are assumed, then the test statistics is

We are given,

Then, assuming H₀ is true, the test statistics is

The critical values for t₃₀ at a 0.01 level of significance are -2.750, 2.750.

As the test statistics does not lie between the critical values, we have sufficient evidence to reject H₀.