In an article in Marketing Science , Silk and Berndt investigate the output of a

Question

In an article in Marketing Science, Silk and Berndt investigate the output of advertising agencies. They describe ad agency output by finding the shares of dollar billing volume coming from various media categories such as network television, spot television, newspapers, radio, and so forth.

(a) Suppose that a random sample of 406 U.S. advertising agencies gives an average percentage share of billing volume from network television equal to 7.45%, and assume that equals 1.44 percent. Calculate a 95% confidence interval for the mean percentage share of billing volume from network television for the population of all U.S. advertising agencies. (Round your answers to 3 decimal places.)

The 95% confidence interval is            [ , ].

(b) Suppose that a random sample of 406 U.S. advertising agencies gives an average percentage share of billing volume from spot television commercials equal to 12.42%, and assume that equals 1.50 percent. Calculate a 95% confidence interval for the mean percentage share of billing volume from spot television commercials for the population of all U.S. advertising agencies. (Round your answers to 3 decimal places.)

The 95% confidence interval is            [ , ].

Explanation / Answer

a)

margin of error = 1.96 * 1.44/sqrt(406) = 0.1401

lower bound = 7.45 - 0.1401 = 7.310

upper bound = 7.45 + 0.1401 = 7.590

b)

margin of error = 1.96 * 1.5/sqrt(406) = 0.1459

lower bound = 12.42 - 0.1459 = 12.274

upper bound = 12.42 + 0.1459 = 12.566

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