Question

A company that produces and markets continuing education programs on DVDs for the educational testing industry has traditionally mailed advertising to prospective customers .A market research study was undertaken to compare two approaches: mailing a sample DVD upon request that contain highlights of the full DVD and sending an email containing a link for a website from which sample material could be downloaded. Of those who responded to either the mailing or the e-mail, the results were as follows in terms of purchase of the complete DVD .

                                    Type of media used

             Purchased                mailing                  E-mail                     total

                   Yes                            26                             11                                 37

                   No                             227                          247                               474

                   Total                         253                          258                               511

a)     at the 0.5 level significance, is there evidence of a difference in the proportion of DVDs purchased in the proportion of DVDs   purchased on the basis of the media used ?

b)     on the basis of the results of (a) which type of media should the company use in the future ? explain the rationale for your decision

The company also wanted to determine which of three sales approaches should be used to generate sales among those who either requested the sample DVD by mail or downloaded the sample DVD but did not purchase the full DVD : 1) targeted e-mail , 2) A DVD that contain additional features or 3) a telephone call to prospective customers. The 474 respondents who did not initially purchase the full DVD were randomly assigned to one of the three sales approaches. The results in terms of purchases of the full program DVD, are as follows:

                                                                                 Sales approach

ACTION                     Targeted            More complete          Telephone calls     Total

                                     Email                       DVD

Purchase                          5                       17                                     18                       40

Do not purchase            153                   141                                   140                      434

Total                                158                    158                                   158 474

c)      at the 0.05 level of significance, is there evidence of a difference in the proportion of DVDs purchased on the basis of the sales strategy used?

d)     On the basis of the results of (c) which sales approach do you think the company should use in the future . Explain the rationale for your decision.

Answer 1

We are given the following data and are asked to test the hypothesis that there is a difference in the proportion of DVDs purchased on the basis of media used.

Purchased	mailing	e-mail	total
Yes	26	11	37
No	227	247	474
total	253	258	511

Given x1=26, x2=11,n1=253,n2=258

p1=x1/n1=0.10,p2=x2/n2=11/258=0.04

Since P is not known

Q=1-P=1-0.07=0.93

Null hypothesis

i.e., there is no difference in the proportions of DVDs purchased on the basis of media used.

Alternate hypothesis

i.e., there is a difference in the proportion of DVDs purchased on the basis of media used.

Test statistic under H₀

Inference

Since test statistic value is greater than 3, we reject the null hypothesis irrespective of the critical value.

Hence we conclude that there is a difference in the proportion of DVDs purchased on the basis of media used.

b) The company should mailing because customers purchased DVDs more using mailing as the media.

Note:- Didn't do the other ones because I wasn't sure about the other two