Question

A marketing firm wishes to test the effectiveness of the audio/visual presentation of certain information as opposed to the purely audio presentation of the information. To this end 100 volunteers were given a 10 minute presentation in which the information was presented in an audio/visual format. A second group of 100 volunteers was presented the same information in a purely audio format. Each person in each of the two groups was asked the same 20 questions related to the information in the presentation.   The audio/visual group had an average of 10.5 correct responses with a sample standard deviation of 4. The purely audio group had an average of 9.4 correct responses with a standard deviation of 3. The marketing firm believes this means that the audio/visual format leads to better retention of the information. We test the hypotheses

H₀: μ ₁ - μ ₂=0 versus H_a: μ ₁ - μ ₂>0

at a 1% level of significance.   Here denotes μ ₁ the population average number of correct responses for individuals presented the information in an audio/ visual format and μ ₂ denotes the population average number of correct responses for individuals presented the information in a purely audio format. Compute the critical value.

Answer 1