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, newspaper, radio, and so forth.

1. Suppose that a random sample of 400 U.S. advertising agencies gives an average percentage share of billing volume from network television equal to 7.46 percent with a standard deviation of 1.42 percent. Calculate a 95 percent confidence interval for the mean percentage share of billing volume from network television for the population of all U.S. advertising agencies.
2. Suppose that a random sample of 400 U.S. advertising agencies gives an average percentage share of billing volume from spot television commercials equal to 12.44 percent with a standard deviation of 1.55 percent. Calculate a 95 percent confidence interval for the mean percentage share of billing volume from spot television commercials for the population of all U.S. advertising agencies.

   Confidence Interval Estimate for the Mean
   Data
   Sample Standard Deviation	1.55
   Sample Mean	12.44
   Sample Size	400
   Confidence Level	95%
   Intermediate Calculations
   Standard Error of the Mean	0.0775
   Degrees of Freedom	399
   t Value	1.965927368
   Interval Half Width	0.152359371
   Confidence Interval
   Interval Lower Limit	12.29
   Interval Upper Limit	12.59

   The 95% CI is therefore (12.29, 12.59).
3. Compare the confidence intervals in part a) and b). Does it appear that the mean percentage share of billing volume from spot television commercials for the U.S. advertising agencies is greater than the mean percentage share of billing volume from network television? Explain.

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