William R. Dillon. Thomas J. Madden1 and Neil H. Firtle discuss a corporate image study designed to find out whether perceptions of technical support services vary depending on the position of the respondent in the organization. The management of a company that suµµlies telephone cable to telephone companies commissioned a media campaign primarily designed to
(l) Increase awareness of the company and (2) create favorable perceptions of the company's technical support. The campaign was targeted to purchasing managers and technical managers at independent telephone companies with greater than 10.000 trunk lines.
Perceptual ratings were measured with a nine-point agree-disagree scale. Suppose the results of a telephone survey of 175 technical managers and 125 purchasing managers reveal that the mean perception score for technical managers is 7.3 and that the mean perception score for purchasing managers is 8.2.
a. Let µ1 be the mean perception score for all purchasing managers and let µ2 be the mean perception score for all technical managers. Set uµ the null and alternative hypotheses needed to establish whether the mean perception scores for purchasing managers and technical managers differ. If µ1 and µ2 do not differ, what does µ1 - µ2 equal?
b. Assuming that the samples of 175 technical managers and 125 Purchasing managers are independent random samples, test the hypotheses you set up in part a by using a critical value with α = .05. Assume here that σ1 = 1.6 and σ2 = 1.4. What do you conclude about whether the mean perception scores for purchasing managers and technical managers differ?
c. Find the p-value for testing the hypotheses you set up in part a. Use the p-value to test these hypotheses by setting a equal to .101 .051 .011 and .001. How much evidence is there that the mean perception scores for purchasing managers and technical managers differ?
d. Calculate a 99 percent confidence interval for µ1 - µ2. Interpret this interval.