You wish to test the following claim (Ha) at a significance level of a = 0.10. Ho: μ = 87.1 H„ : μ < 87.1 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 54.5 56.5 67.6 30.4 83.3 102.2 What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... O less than (or equal to) a O greater than a This test statistic leads to a decision to... O reject the null O accept the null fail to reject the null

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### Hypothesis Testing at a Significance Level of \( \alpha = 0.10 \)

You wish to test the following claim (\( H_a \)) at a significance level of \( \alpha = 0.10 \):

\[ H_0: \mu = 87.1 \]
\[ H_a: \mu < 87.1 \]

You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

| data  |
|-------|
| 54.5  |
| 56.5  |
| 67.6  |
| 30.4  |
| 83.3  |
| 102.2 |

1. **Test Statistic Calculation**

   What is the test statistic for this sample? (Report answer accurate to three decimal places.)

   \[ \text{test statistic} = \_\_\_\_\_\_\_\_ \]

2. **P-value Calculation**

   What is the p-value for this sample? (Report answer accurate to four decimal places.)

   \[ \text{p-value} = \_\_\_\_\_\_\_\_ \]

3. **Decision Making**

   The p-value is...
   - ☐ less than (or equal to) \( \alpha \)
   - ☐ greater than \( \alpha \)

### Conclusion

This test statistic leads to a decision to...
- ☐ reject the null
- ☐ accept the null
- ☐ fail to reject the null
Transcribed Image Text:### Hypothesis Testing at a Significance Level of \( \alpha = 0.10 \) You wish to test the following claim (\( H_a \)) at a significance level of \( \alpha = 0.10 \): \[ H_0: \mu = 87.1 \] \[ H_a: \mu < 87.1 \] You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: | data | |-------| | 54.5 | | 56.5 | | 67.6 | | 30.4 | | 83.3 | | 102.2 | 1. **Test Statistic Calculation** What is the test statistic for this sample? (Report answer accurate to three decimal places.) \[ \text{test statistic} = \_\_\_\_\_\_\_\_ \] 2. **P-value Calculation** What is the p-value for this sample? (Report answer accurate to four decimal places.) \[ \text{p-value} = \_\_\_\_\_\_\_\_ \] 3. **Decision Making** The p-value is... - ☐ less than (or equal to) \( \alpha \) - ☐ greater than \( \alpha \) ### Conclusion This test statistic leads to a decision to... - ☐ reject the null - ☐ accept the null - ☐ fail to reject the null
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