Use a significance level ofa=0.05 to test the claim that u = 19.6. The sample data consists of 10 scores for which x =20.1 and s=4.1. state the null and alternative hypotheses, compute the value of the test statistic, and find the P-value for the sample. Sstate your conclusions about the claim. H :H= 19.6 H, : µz19.6 OTest statistic: t=0.3856. P-Value: P=0.7087. Reject H, :H = 19.6. Since P>a, there is sufficient evidence to support the claim that the mean is different from 19.6. H: H= 20.1 H : µz 20.1 O Test statistic: t=20.1. P-Value: P= 0.7087. Accept Ho H = 20.1. Since P>a, there is not sufficient evidence to support the claim that the mean is different from 20.1. H:u= 19.6 Huz19.6
Use a significance level ofa=0.05 to test the claim that u = 19.6. The sample data consists of 10 scores for which x =20.1 and s=4.1. state the null and alternative hypotheses, compute the value of the test statistic, and find the P-value for the sample. Sstate your conclusions about the claim. H :H= 19.6 H, : µz19.6 OTest statistic: t=0.3856. P-Value: P=0.7087. Reject H, :H = 19.6. Since P>a, there is sufficient evidence to support the claim that the mean is different from 19.6. H: H= 20.1 H : µz 20.1 O Test statistic: t=20.1. P-Value: P= 0.7087. Accept Ho H = 20.1. Since P>a, there is not sufficient evidence to support the claim that the mean is different from 20.1. H:u= 19.6 Huz19.6
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
Transcribed Image Text:**Hypothesis Testing: Determining the Statistical Significance**
**Problem Statement:**
Use a significance level of \( \alpha = 0.05 \) to test the claim that \( \mu = 19.6 \). The sample data consists of 10 scores for which \( \bar{x} = 20.1 \) and \( s = 4.1 \). State the null and alternative hypotheses, compute the value of the test statistic, and find the P-value for the sample. State your conclusions about the claim.
**Step-by-Step Solution:**
1. **State the Null and Alternative Hypotheses:**
- \( H_0: \mu = 19.6 \)
- \( H_1: \mu \neq 19.6 \)
2. **Compute the Test Statistic and P-Value:**
- Test Statistic: \( t = 0.3856 \)
- P-Value: \( P = 0.7087 \)
Since \( P > \alpha \), there is sufficient evidence to support the claim that the mean is different from 19.6.
Conclusion: Reject \( H_0: \mu = 19.6 \).
3. **Second Set of Hypotheses:**
- \( H_0: \mu = 20.1 \)
- \( H_1: \mu \neq 20.1 \)
4. **Compute the Test Statistic and P-Value:**
- Test Statistic: \( t = 20.1 \)
- P-Value: \( P = 0.7087 \)
Since \( P > \alpha \), there is not sufficient evidence to support the claim that the mean is different from 20.1.
Conclusion: Accept \( H_0: \mu = 20.1 \).
5. **Third Set of Hypotheses:**
- \( H_0: \mu = 19.6 \)
- \( H_1: \mu \neq 19.6 \)
**Graphical Representation:**
Unfortunately, the image provided does not contain a graphical representation. If there were graphs or diagrams, they would typically show:
- A t-distribution curve to illustrate the position of the test statistic and shaded area representing the P-value.
- A visual comparison between the sample mean and the hypothesized population mean.
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