Answered: 1. A researcher wants to select a… | bartleby

MATLAB: An Introduction with Applications

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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1. Stating whether the test is a one-tailed or two-tailed test

2. Stating the correct Null and Alternative Hypotheses

3. Stating the alpha (z-value from the unit normal table) for the boundary of the critical region for a one-tailed test or two-tailed test

4. Calculating \(\sigma_M\)

5. Calculating the test statistic (z-score)

### Hypothesis Testing: One-Tailed Test Example

**1. Scenario Description**

A researcher wants to select a sample from a population with a mean (\(\mu\)) = 60 and administer a treatment to individuals in the sample. He thinks the treatment will help improve scores.

a. **State the hypotheses for a one-tailed test.**

b. **For a one-tailed test, would the critical region be located in the positive or right-hand tail of the distribution, or in the negative or left-hand tail of the distribution?**

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In this scenario, the researcher is aiming to determine whether the treatment improves the scores beyond the population mean of 60. This type of hypothesis testing is focused on detecting an increase in scores, thus a one-tailed test is appropriate. Typically, for such tests:

- **Null Hypothesis (\(H_0\))**: The mean score after treatment is less than or equal to 60.
- **Alternative Hypotheses (\(H_1\))**: The mean score after treatment is greater than 60.

Since the researcher believes the treatment will improve scores, the critical region will be located in the positive or right-hand tail of the distribution. This indicates an expectation of results that are significantly greater than the population mean.

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