Hey i needed help on this question...i am very confused
The marketing manager is interested in her companys market share (a pro-
portion) before and after an advertising campaign. In order to assess the
effectiveness of the proposed campaign a simple random sample of n1 shop-
pers is to be taken, before the campaign, from which the proportion, P1; who
currently buy the companys product will be obtained. Similarly, following a
sufficient period after the advertising campaign, a different random sample of
n2 shoppers is to be taken from which the proportion, P2; who then buy the
product will be obtained. Let Pi1 and Pi2 denote the true population market
shares for the company?s product before and after the advertising campaign,
Answer the following questions:
(a) What is E [P1 - P2] ?
(b) What is var [P1 - P2] ?
(c) What is the approximate sampling distribution of P1 - P2 ?
Now suppose that the null hypothesis, H0; is that the advertising cam-
paign had no effect on the companys market share; i.e., H0 : Pi1 = Pi2 = Pi;
say. Under the assumption that H0 is true, answer the following ques-
(d) What is E [P1 - P2] ?
(e) What is var [P1 - P2] ?
(f) What is the approximate sampling distribution of P1 - P2 ?
(g) How would you estimate Pi using the data from both samples ?
(h) Similarly, how would you estimate var [P1 - P2] ?
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- Thread Starter
- 08-04-2011 01:32
- 08-04-2011 01:57
E[P1-P2] = Pi1 -Pi2, a standard result.
You have the result for Var[P1 - P2] in terms of Pi1, Pi2, n1 and n2 ?
- Thread Starter
- 08-04-2011 22:05
- 08-04-2011 22:33
Var[P1 - P2] = Pi1( 1 - Pi1 )/n1 + Pi2( 1 - Pi2 )/n2
P1-P2 would be approx normal assuming n1 and n2 were reasonably sized...