Answered: For which of the following is a t-test…

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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For which of the following is a t-test appropriate for performing a hypothesis test?

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A simple random sample of 11 movies is taken from the collection of movies at a rental store with approximately normally distributed time lengths. The sample mean is 118 minutes and the sample standard deviation is 8 minutes.

A sample mean of 194 pages and a standard deviation of 27 pages are obtained using a simple random sample of the lengths (pages) of 13 books from a public library.

A sample mean of 45,413 dollars and a standard deviation of 5,436 dollars are obtained using a convenient sample of 26 individuals from the residents of a town, which have approximately normally distributed incomes.

A population is approximately normal with standard deviation 2. The sample mean is 76, and the sample standard deviation is 5 based on a simple random sample of size 17.

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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