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 400 U.S. advertising agencies gives an average percentage share of billing volume from network television equal to 7.46 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. b. Suppose that a random sample of 400 U.S. advertising agencies gives an average percentage share of billing volume from spot television commercials equal to 12.44 percent, and assume that σ equals 1.55 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. 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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 400 U.S. advertising agencies gives an average
percentage share of billing volume from network television equal to 7.46 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.
b. Suppose that a random sample of 400 U.S. advertising agencies gives an average
percentage share of billing volume from spot television commercials equal to 12.44 percent,
and assume that σ equals 1.55 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.
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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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