Question

n 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 398 U.S. advertising agencies gives an average percentage share of billing volume from network television equal to 7.43 percent, and assume that σ 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. (Round your answers to 3 decimal places.) The 95 percent confidence interval is [, ].

(b) Suppose that a random sample of 398 U.S. advertising agencies gives an average percentage share of billing volume from spot television commercials equal to 12.45 percent, and assume that σ equals 1.51 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 3 decimal 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).

Answer 1

a)

E = margin of Error=z*sd/sqrt(n)

CI=mean+/-E

mean	7.43
sigma	1.42
n	398
standard error	0.071178
margin of error	0.139509
lower	7.290491
upper	7.569509

b)

mean	12.45
sigma	1.51
n	398
standard error	0.075689
margin of error	0.148351
lower	12.30165
upper	12.59835

c) confidence interval in (b) is totally greater than the confidence interval in (a).

hence

it appears 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