MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Transcribed Image Text:**Testing the Mean of Differences for Paired Data**
To test the claim about the mean of the differences for a population of paired data at the specified level of significance (\(\alpha\)), assume the samples are random and dependent, and the populations are normally distributed.
**Claim:** \(\mu_d \geq 0\)
**Level of Significance:** \(\alpha = 0.10\)
**Sample Statistics:**
- Mean of differences (\(\bar{d}\)) = -2.4
- Standard deviation of differences (\(s_d\)) = 1.4
- Sample size (\(n\)) = 14
**Hypothesis Options:**
A.
- \(H_0: \mu_d < 0\)
- \(H_a: \mu_d \geq 0\)
B.
- \(H_0: \mu_d \geq 0\)
- \(H_a: \mu_d < 0\)
C.
- \(H_0: \mu_d \leq 0\)
- \(H_a: \mu_d > 0\)
D.
- \(H_0: \mu_d = 0\)
- \(H_a: \mu_d \neq 0\)
E.
- \(H_0: \mu_d = 0\)
- \(H_a: \mu_d > 0\)
F.
- \(H_0: \mu_d = 0\)
- \(H_a: \mu_d \neq 0\)
**Explanation:**
This test involves determining if the mean difference (\(\mu_d\)) is significantly different from the hypothesized claim (\(\geq\) 0). Each option presents a set of null (\(H_0\)) and alternative (\(H_a\)) hypotheses, allowing for different possibilities based on the claim being tested.
Choose the correct hypothesis set that aligns with evaluating whether the mean of the differences is greater than or equal to zero.
Transcribed Image Text:### Hypothesis Testing for Paired Data
**Claim: μ₀ ≥ 0; α = 0.10. Sample statistics:**
- \( \bar{d} = -2.4 \)
- \( s_d = 1.4 \)
- n = 14
**Test the Claim:**
This section guides you through evaluating the mean differences for a population of paired data at the given significance level (α = 0.10). It assumes random and dependent samples with normally distributed populations.
1. **Test Statistic:**
- Calculate the test statistic \( t \) using the given sample statistics. (Round to two decimal places as needed.)
2. **P-Value:**
- Determine the P-value associated with the test statistic. (Round to three decimal places as needed.)
3. **Decision Making:**
- Compare the P-value with the level of significance (α).
- If the P-value is less than α, reject the null hypothesis.
- Make a conclusion based on statistical evidence.
This setup helps in understanding hypothesis testing scenarios dealing with paired samples. To complete these steps, use standard formulas for hypothesis tests involving means of paired data.
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