Answered: Suppose you are a television network…

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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Question

Suppose you are a television network executive interested in how a new pilot show, Stat1stics, will be received by the general US television-viewing population. You hire several market research firms; each recruits a random sample of television viewers and asks them to watch the pilot of Stat1stics. Each firm then gathers 16 respondents and asks each of them, “On a scale of 1 to 10, where 1 means you’ll never watch Stat1stics again, and 10 means you expect to never miss an episode of Stat1stics, how do you rate Stat1stics?”

Assume that if you asked every member of the general US television-viewing population about the pilot, the mean response would be 4.0 with a standard deviation of 1.5.

Each market research firm reports the mean rating of its random sample. Assume each market research firm recruits a different sample, and that you hired exactly enough market research firms such that all possible samples of 16 US television viewers were sampled and their mean ratings reported.

Which of the following are true about the sampling distribution of the mean ratings reported to you by the market research firms? Check all that apply.

The mean of the distribution of mean ratings is 0.25.

The shape of the distribution of mean ratings is approximately normal.

The shape of the distribution of mean ratings depends on the shape of the ratings of the general US television-viewing population.

The standard deviation of the distribution of mean ratings is 0.38.

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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