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

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 390 U.S. advertising agencies gives an average percentage share of billing volume from network television equal to 7.45 percent, and assume that sigma equals 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. The 95 percent confidence interval is [, ] (b) Suppose that a random sample of 390 U.S. advertising agencies gives an average percentage share of billing volume from spot television commercials equal to 12.42 percent, and assume that sigma equals 1.59 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. The 95 percent confidence interval is [, ] (c) Compare the confidence intervals in parts a and b. Does it appear that the mean percentage share of billing volume from spot television commercials for U.S. advertising agencies is greater than the mean percentage share of billing volume from network television? Explain., confidence interval in (b) is totally the confidence interval in (a).

Explanation / Answer

a) The statistical software output for this problem is:

One sample Z confidence interval:
: Mean of population
Standard deviation = 1.42

95% confidence interval results:

Hence,

The 95 percent confidence interval is [7.309, 7.591]

b) The statistical software output for this problem is:

One sample Z confidence interval:
: Mean of population
Standard deviation = 1.59

95% confidence interval results:

Hence,

The 95% confidence interval is [12.262, 12.578]

c) Yes, confidence interval is (b) is totally different from the confidence interval is (a).

Not sure about the choice of second dropdown but since i dont know the options, i can't make a right call in this.

Mean n Sample Mean Std. Err. L. Limit U. Limit 390 7.45 0.071904495 7.3090698 7.5909302

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