Answered: graduate student is performing a study…

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 graduate student is performing a study on a new anti-anxiety drug. The drug is supposed to reduce anxiety, but the graduate student realizes that it may do nothing or even increase anxiety, so he decides to formulate nondirectional hypotheses and conduct a two-tailed test. He knows that the average score for all anxious people is μ₀ = 15, with a standard deviation of σ = 4. If he designates the mean for the population of anxious people who take the anti-anxiety drug as μanti-anxiety druganti-anxiety drug, he can identify the null and alternative hypotheses as:

	H₀: μanti-anxiety druganti-anxiety drug = μ₀
	H₁: μanti-anxiety druganti-anxiety drug ≠ μ₀

The sample of 64 anxious people who tried out the new anti-anxiety drug scored an average of 14.1.

Since the graduate student knows the standard deviation of the scores on the anxiety inventory for the population of people who are anxious, he intends to use a hypothesis test that uses the z-score of the sample mean as the test statistic (also known as the z test). First, he wants to make sure all the required assumptions are satisfied. Which of the following conditions is not a required assumption for the z test?

The mean of the scores on the anxiety inventory is the same for those who take the anti-anxiety drug and those who don’t.

The standard deviation of the scores on the anxiety inventory is the same for those who take the anti-anxiety drug and those who don’t.

Each observation is independent of every other observation.

Members of the sample are selected randomly.

The scores on the anxiety inventory follow a normal distribution or the sample size is large (at least 30).

Use the Distributions tool to find the critical region for α = 0.05.

Standard Normal Distribution

Mean = 0.0

Standard Deviation = 1.0

-4-3-2-101234z.2500.5000.2500-0.6740.674

The critical z-scores (the values for z-scores that separate the tails from the main body of the distribution, forming the critical regions) are .

Calculate the z statistic, and use the Distributions tool to evaluate the null hypothesis. The z statistic is . The z statistic lie in the critical region for a two-tailed hypothesis test. Therefore, the null hypothesis is .

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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