Answered: Samples of size 2 200- Samples of size…

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

A study measured the waist size of 970 men, finding a mean of 36.33 inches and a standard deviation of

3.91 inches. A histogram of these measurements is shown to the right.

a) Describe the histogram of the waist sizes.

b) To explore variation of the mean from sample to sample, they simulated by drawing many samples of size 2, 5, 10, and 20 with replacement, from the 970 measurements. The histograms for each simulation are shown in the accompanying table. Explain how these histograms demonstrate what the Central Limit Theorem says about the sampling distribution model for sample means.

a) Choose the correct answer below.

A. The histogram is skewed to the right.

B. The histogram is skewed to the left.

C. The histogram is symmetric.

b) These simulations ▼(appear/do not appear) to demonstrate what the Central Limit Theorem says about the sampling distribution model for sample means. All of the histograms are centered near 36 inches. As n gets larger, the histograms ▼ (become less Normal/ stay approximately the same/approach the Normal shape), and the variability in the sample means ▼ (stays approximately the same/ decreases/ increases. The histograms ▼ (are fairly Normal? are skewed left/ are skewed right by the time the sample reaches size 5.

Samples of size 2
200-
Samples of size 5
150-
100-
100-
50어
28
Sample Mean Waist Size
42
30
Sample Mean Waist Size
Samples of size 10
200-
Samples of size 20
200-
100-
100-
o+
32
Sample Mean Waist Size
32
Sample Mean Waist Size
# of Samples
# of Samples
# of Samples
#of Samples

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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