Answered: If you were really a television network…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

If you were really a television network executive, you would not hire multiple market research firms to each recruit a different sample of respondents. Instead, you would likely hire only one market research firm. If this is the case, why should you care about the theoretical distribution of mean ratings of multiple samples if you are only going to hire one firm and get one sample and one mean from that sample?

To draw conclusions about the population mean using a sample mean, you need to know the theoretical distribution of the possible values the sample mean ratings could have.

You need to know the theoretical distribution of possible values of the sample mean ratings to know whether the market research firm recruited the right sample.

You should not care about the possible distribution of mean ratings. You should only care about the mean and perhaps the highest and lowest ratings.

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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