Answered: Assume that we want to construct 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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Assume that we want to construct a confidence interval. Do one of thefollowing, as appropriate: (a) find the critical value

tα/2,

(b) find the critical value

zα/2,

or (c) state that neither the normal distribution nor the t distribution applies.

The confidence level is

90%,

is not known, and the normal quantile plot of the

salaries (in thousands of dollars) of basketball players on a team is as shown.

I DIDN'T MEAN TO SELECT 'A'

**Constructing a Confidence Interval**

Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value $ t_{\alpha/2} $, (b) find the critical value $ z_{\alpha/2} $, or (c) state that neither the normal distribution nor the t distribution applies.

The confidence level is 90%, $\sigma$ is not known, and the normal quantile plot of the 17 salaries (in thousands of dollars) of basketball players on a team is as shown.

**Graph Description:**

A normal quantile plot displays the z scores of the data. It shows a line with a slope that generally increases to the top right of the plot. The x-axis represents the x values (salaries), ranging from approximately 0 to 21,000. The y-axis represents the z score, ranging from -2 to 2.

The data points (blue dots) are somewhat aligned along the diagonal line, indicating a pattern that resembles normal distribution characteristics, but it is not perfectly followed throughout the distribution.

**Multiple Choice Options:**

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. $ t_{\alpha/2} = $ □
(Round to two decimal places as needed.)

B. $ z_{\alpha/2} = $ □
(Round to two decimal places as needed.)

C. Neither the normal distribution nor the t distribution applies.

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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