MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Q25. Using the Pearson correlation coefficient, a study on addiction found a positive correlation between time of cravings and time of relapse (r = .51) in a sample of 20 people with a drug addiction. Using a two-tailed test at a .05 level of significance, test whether the correlation is significantly different than 0. Follow the prompts.

Step 1. State the hypotheses.

A

B

C

D

Step 2. Find the critical values. df = _______

CV = +/- (do not include +/-) DO NOT USE eTEXT TABLE C.5 - CVs ARE WRONG. Use table attached to homework instead. _________

Step 4. Make a decision about the null hypothesis.

a. Reject H0
b. Retain H0
 
 
### Hypothesis Testing Examples

Here are four examples of null and alternative hypotheses, represented by \( H_0 \) and \( H_1 \), respectively:

#### (A)
- **Null Hypothesis (\( H_0 \))**: \( \rho = 0.51 \)
- **Alternative Hypothesis (\( H_1 \))**: \( \rho \neq 0.51 \)

#### (B)
- **Null Hypothesis (\( H_0 \))**: \( \rho = 0 \)
- **Alternative Hypothesis (\( H_1 \))**: \( \rho \neq 0 \)

#### (C)
- **Null Hypothesis (\( H_0 \))**: \( \rho \neq 0 \)
- **Alternative Hypothesis (\( H_1 \))**: \( \rho = 0 \)

#### (D)
- **Null Hypothesis (\( H_0 \))**: \( \rho \neq 0.51 \)
- **Alternative Hypothesis (\( H_1 \))**: \( \rho = 0.51 \)

These examples illustrate how hypotheses can be structured to test specific claims about a parameter, such as a correlation coefficient (\( \rho \)) in a population.
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Transcribed Image Text:### Hypothesis Testing Examples Here are four examples of null and alternative hypotheses, represented by \( H_0 \) and \( H_1 \), respectively: #### (A) - **Null Hypothesis (\( H_0 \))**: \( \rho = 0.51 \) - **Alternative Hypothesis (\( H_1 \))**: \( \rho \neq 0.51 \) #### (B) - **Null Hypothesis (\( H_0 \))**: \( \rho = 0 \) - **Alternative Hypothesis (\( H_1 \))**: \( \rho \neq 0 \) #### (C) - **Null Hypothesis (\( H_0 \))**: \( \rho \neq 0 \) - **Alternative Hypothesis (\( H_1 \))**: \( \rho = 0 \) #### (D) - **Null Hypothesis (\( H_0 \))**: \( \rho \neq 0.51 \) - **Alternative Hypothesis (\( H_1 \))**: \( \rho = 0.51 \) These examples illustrate how hypotheses can be structured to test specific claims about a parameter, such as a correlation coefficient (\( \rho \)) in a population.
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