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.