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 396 U.S. advertising agencies gives an average percentage share of billing volume from network television equal to 7.48%, and assume that o equals 1.49 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 ( D O ) (b) Suppose that a random sample of 396 U.S. advertising agencies gives an average percentage share of billing volume from spot television commercials equal to 12.49%, and assume that o equals 1.55 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. above the (Yes , confidence interval in (b) is totally confidence interval in (a).

Answer 1

Answer Date: 11/11/2019 The 95% confidence interval for the mean percentage share of billing volume from network television for the population of all U.S. advertising agencies is, First, compute z-critical value then find confidence interval. The z-critical value is, From the standard normal table, the z-critical value at 95% confidence is 1.960. 95%C.I.= plizxo/In = 7.48 +1.960 x1.49/1396 = 7.48 +0.147 = 7.333 to 7.627 The 95% confidence interval for the mean percentage share of billing volume from network television for the population of all U.S. advertising agencies is 7.333 to 7.627

b) The 95% confidence interval for the mean percentage share of billing volume from spot television for the population of all U.S. advertising agencies is, First, compute z-critical value then find confidence interval. The Z-critical value is, From the standard normal table, the z-critical value at 95% confidence is 1.960. 95% C.I.= uliz, xo/ In = 12.49 -1.960 x1.55/1396 = 12.49 +0.153 = 12.337 to 12.643 The 95% confidence interval for the mean percentage share of billing volume from spot television for the population of all U.S. advertising agencies is 12.337 to 12.643