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 401 U.S. advertising agencies gives an average percentage share of billing volume from network television equal to 7.47 percent, and assume that o equals 1.48 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. (Round your answers to 3 decimal places.) ______ The 95 percent confidence interval is [________. _______]) b. Suppose that a random sample of 401 U.S. advertising agencies gives an average percentage share of billing volume from spot television commercials equal to 12.42 percent, and assume that o equals 1.58 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. (Round your answers to places.) 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

Solution:-

The Confidence Interval formula is

Where:

Here z = 1.96, coresponding to 95% confidence interval

Given, Mean = 7.47

Using the formula,

7.47 + 1.96 * 1.48/sqrt(401)

7.47 ± 0.145

7.325 to 7.615

b). Given, Mean = 12.42

s = 1.58

Using the formula,

12.42 + 1.96 * 1.58 / sqrt(401)

12.42 + 0.155

12.265 to 12.574

X ± Z s (n)

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