Use the following Distributions tool to identify the boundaries that separate the extreme samples from the samples that are more obviously consistent with the null hypothesis. Assume the null hypothesis is nondirectional, meaning that the critical region is split across both tails of the distribution. The z-score boundaries at an alpha level α = .05 are: z = 1.96 and z = –1.96 z = 3.29 and z = –3.29 z = 2.58 and z = –2.58 To use the tool to identify the z-score boundaries, click on the icon with two orange lines, and slide the orange lines until the area in the critical region equals the alpha level. Remember that the probability will need to be split between the two tails. To use the tool to help you evaluate the hypothesis, click on the icon with the purple line, place the two orange lines on the critical values, and then place the purple line on the z statistic. Standard Normal Distribution Mean = 0.0 Standard Deviation = 1.0 -4-3-2-101234z.2500.5000.2500-0.670.67 The critical region is . The z-score boundaries for an alpha level α = 0.01 are: z = 1.96 and z = –1.96 z = 3.29 and z = –3.29 z = 2.58 and z = –2.58 Suppose that the calculated z statistic for a particular hypothesis test is 2.00 and the alpha is 0.01. This z statistic is the critical region. Therefore, the researcher reject the null hypothesis, and he conclude the alternative hypothesis is probably correct.

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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3. Alpha level and the critical region

The alpha level that a researcher sets at the beginning of the experiment is the level to which he wishes to limit the probability of making the error of .

Use the following Distributions tool to identify the boundaries that separate the extreme samples from the samples that are more obviously consistent with the null hypothesis. Assume the null hypothesis is nondirectional, meaning that the critical region is split across both tails of the distribution.

The z-score boundaries at an alpha level α = .05 are:

z = 1.96 and z = –1.96

z = 3.29 and z = –3.29

z = 2.58 and z = –2.58

To use the tool to identify the z-score boundaries, click on the icon with two orange lines, and slide the orange lines until the area in the critical region equals the alpha level. Remember that the probability will need to be split between the two tails.

To use the tool to help you evaluate the hypothesis, click on the icon with the purple line, place the two orange lines on the critical values, and then place the purple line on the z statistic.

Standard Normal Distribution

Mean = 0.0

Standard Deviation = 1.0

-4-3-2-101234z.2500.5000.2500-0.670.67

The critical region is .

The z-score boundaries for an alpha level α = 0.01 are:

z = 1.96 and z = –1.96

z = 3.29 and z = –3.29

z = 2.58 and z = –2.58

Suppose that the calculated z statistic for a particular hypothesis test is 2.00 and the alpha is 0.01. This z statistic is the critical region. Therefore, the researcher reject the null hypothesis, and he conclude the alternative hypothesis is probably correct.

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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