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 405 U.S. advertising agencies gives an average percentage share of billing volume from network television equal to 7.42%, and assume that σ 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 405 U.S. advertising agencies gives an average percentage share of billing volume from spot television commercials equal to 12.40%, and assume that σ equals 1.56 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            [, ].

(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.

(Click to select)YesNo , confidence interval in (b) is totally (Click to select)belowabove the confidence interval in (a).

Answer 1

Formula for Confidence Interval for population Mean When Population Standard deviation is known

a. Given

Given
Sample average percentage share of billing volume from network television : Sample Mean :	7.42
Population Standard Deviation :	1.44
Number of U.S. advertising agencies in the sample Sample Size : n	405
Confidence Level :	95
: (100-95 )/100	0.05
/2	0.025
Z0.025	1.96

95% confidence interval for the mean percentage share of billing volume from network television for the population of all U.S. advertising agencies

95% confidence interval for the mean percentage share of billing volume from network television for the population of all U.S. advertising agencies : (7.2798,7.5602)

b.

Given
Sample average percentage share of billing volume from spot television commercials : Sample Mean :	12.40
Population Standard Deviation :	1.56
Number of U.S. advertising agencies in the sample Sample Size : n	405
Confidence Level :	95
: (100-95 )/100	0.05
/2	0.025
Z0.025	1.96

95% confidence interval for the mean percentage share of billing volume from spot television commercials for the population of all U.S. advertising agencies

95% confidence interval for the mean percentage share of billing volume from spot television commercials for the population of all U.S. advertising agencies : (12.2481,12.5519)

(c)

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

Ans : Yes;

As lower confidence limit of (b) : 12.2481 > Upper confidence limit of (a) : 7.5602

so , the confidence interval in (b) is (12.2481, 12.5519) is totally above the confidence interval in (a) (7.2798,7.5602)

confidence interval in (b) is totally above the confidence interval in (a)

Ans : Yes ; Above