Answered: If the sample size is n=81, find the…

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

Q scores are normally distributed with a mean of 95 and a standard deviation of 18. Assume that many samples of size n are taken from a large population of people and the mean IQ score is computed for each sample.

a. If the sample size is n=81, find the mean and standard deviation of the distribution of sample means.

The mean of the distribution of sample is __

The standard deviation of the distribution of sample means is__ (type an integer or decimal rounded to the nearest tenth as needed)

b. If the sample size is n=169, find the mean and standard deviation of the distribution of sample means.

The mean of distribution of sample means is __

The standard deviation of the distribution of sample means is __ (type an iteger or decimal rounded to the nearest tenth as needed)

c. Why is the standard deviation in part A. different from the standard deviation in part B? Choose the correct answer below

A. With smaller sample sizes (as in part a), the means tend to be further apart, so they have more variation, which results in a smaller standard deviation.

B. With larger sample sizes (as in part b) the means tend to be closer together, so they have less variation, which results in a smaller standard deviation.

C. With larger samples (as in part b) the means tend to be further apart, so they have more variation, which results in a bigger standard deviation.

D. With smaller sample sizes (as in part a) the means tend to be closer together, so they have less variation, which results in a smaller standard deviation.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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