A bank manager has been presented with a new brochure that wasdesigned to be mor

Question

A bank manager has been presented with a new brochure that wasdesigned to be more effective in attracting current customers to apersonal financial counseling session that would include ananalysis of additional banking services that could be advantageousto both bank and the customer. The manager’s assistant, whocreated the new brochure randomly selects 400 current customers,the randomly chooses 200 to receive the standard brochure that hasbeen used in the past, with other 200 receiving the promising newbrochure the he developed. Of those receiving the standardbrochure, 35% call for more information about counseling sessions,while 42% of those receiving the new brochure call for moreinformation. Using the 0.10 level of significance, is it possiblethat the superior performance of the new brochure was due to chanceand that the new brochure might really be no better than the oldone?

Explanation / Answer

p1=0.35 (standard brochure), n1=200 p2=0.42 (new brochure), n2=200 =0.1, Z(0.1)=-1.282 (check normal table) The test hypothesis is Ho:p1p2 The test statistic is Z=(p1-p2)/([p1*(1-p1)/n1] + [p2*(1-p2)/n2]) =(0.35-0.42)/sqrt(0.35*(1-0.35)/200 + 0.42*(1-0.42)/200) =-1.44 Since Z=-1.44 < -1.282, we reject Ho. Thus, we can not say thatthe new brochure might really be no better than the old one.

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