PhStat

Solution Summary

The solution addresses the following in PhStat:

Question 1

The personnel manager of a large insurance company would like to evaluate the effectiveness of four different sales training programs. Eight new recruits are assigned to each of the four training programs A to D. The scores of the members in each group on an exam are recorded below. In answering the questions below you must support your answers with specific numerical output from the Excel analysis.

A B C D
66 72 61 63
74 51 60 61
82 59 57 76
75 62 60 84
73 74 81 58
97 64 55 65
87 78 70 69
78 63 71 80

a) Is there a significant difference between the four groups?
b) Which individual groups differ from each other?
c) What is the within groups variance and why is it part of the calculations?

Question 2

An industrial psychologist wishes to study the effects of motivation on sales in a particular firm. Of 24 new salespersons, 12 are paid an hourly rate and 12 are paid a commission. The 24 individuals are randomly assigned to two groups. The following data represent the sales volume (in thousands of dollars) achieved during the first month on the job.

a) Using a 0.05 level of significance is there evidence of a significant difference in the two groups.
b) Explain what would happen to the findings if the variance of both groups were much larger. Hint: Consult the formula for computing the t or z value in a difference of means test. You could rerun the analysis and compare outputs to answer this question.

Hourly Commission
256 224
212 261
239 254
216 228
222 273
236 234
207 285
219 225
228 237
225 232
241 277
230 245

Question 3

As you know from your marketing studies brand awareness is a key consideration in promotion. An advertising manager wants to know whether the campaign the company is currently running is achieving an average awareness score of 80 or above. He distributes 50 questionnaires to potential buyers. The questionnaire measures brand awareness on a 0-100 scale. The mean score is 82.3 with a standard deviation of 14.1.

a) Set up the null and alternative hypotheses.
b) Determine at the 0.05 level of significance whether the advertising manager has achieved his brand awareness objective.
c) Rerun the analysis in part b but with a sample size of 150. If the conclusion drawn from the analysis is different you must explain why. Hint look at the formula for z or t in a test of a single mean and/or compare your two outputs very carefully.