A marketing firm wishes to test the effectiveness of the audio/visual presenation of certain information as opposed to the purely audio presentation of information. To this end250 volunteers were given a 10 minute presentation in which the information was presented in an audio/visual format. A second group of 250 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 infomrstion in the presentation. The audio/visual grouo had an average of 10.2 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 hypothesed
H1: µ1 – µ2 = 0 versus Ha: µ1-µ>0
at a 2% level of significance. Here µ1 denotes the population average number of correct responses for individuals presented the information in an audio/visual format and µ2 denotes the population average number of correct responses for individuals presented the information in a purely audio format.
Find the critical value for the rejection region.
Compute the test statistic: