Answered: A variable of two populations has a…

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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A variable of two populations has a mean of 55 and a standard deviation of

36 for one of the populations and a mean of 55 and a standard deviation of 10 for the other population. Complete parts (a) through (c).

a. For independent samples of size 9 and 4, respectively, find the mean and standard deviation of x1−x2. (Assume that the sampling is done with replacement or that the population is large enough.)

The mean of x1−x2 is _________

(Type an integer or a decimal. Do not round.)

The standard deviation of x1−x2 is _________

(Round to four decimal places as needed.)

b. Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Choose the correct answer below.

A. No, the variable must be approximately normally distributed on at least one of the two populations for the formulas for the mean and standard deviation of x1−x2to hold, as long as the sampling is done with replacement.

B. No, the variable does not need to be normally distributed for the formulas for the mean and standard deviation of x1−x2 to hold as long as the sample sizes are large enough, as long as the sampling is done with replacement.

C. Yes, the variable must be approximately normally distributed on each of the two populations for the formulas for the mean and standard deviation of x1−x2 to hold.

D. No, the formulas for the mean and standard deviation of x1−x2

hold regardless of the distributions of the variable on the two populations, as long as the sampling is done with replacement or that the population is large enough.

c. Can you conclude that the variable x1−x2 is normally distributed? Explain your answer.

Choose the correct answer below.

A. No, since x1−x2 must be greater than or equal to 0, the distribution is right skewed, so cannot be normally distributed.

B. Yes, x1−x2 is always normally distributed because of the central limit theorem.

C. No, x1−x2 is normally distributed only if x is normally distributed on each of the two populations or if the sample sizes are large enough.

D. Yes, x1−x2 is always normally distributed because it is calculated using parameters.

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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