In a test of Ho: H= 90 against Ha:u> 90, the sample data yielded the test statistic z = 2.17. Find and interpret the p-Value for the test. E Click the icon to view a table of standard normal values The p-value is p= 0.015 (Round to three decimal places as needed.) Interpret the results. What does this p-value mean? O A. The probability of observing a z-value<2.17 is equal to the p-value, if u> 90. O B. The probability of observing a z-value> 2.17 is equal to the p-value, if u > 90. O C. The probability of observing a z-value> 2.17 is equal to the p-value, if u = 90. O D. The probability of observing a z-value<2.17 is equal to the p-value, if u = 90.

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### Hypothesis Testing Example

In a test of \( H_0: \mu = 90 \) against \( H_a: \mu > 90 \), the sample data yielded the test statistic \( z = 2.17 \). Find and interpret the p-value for the test.

#### Instructions:
Click the icon to view a table of standard normal values.

#### Calculation of p-value:
The p-value is \( p = 0.015 \). 
(Round to three decimal places as needed.)

### Interpretation of Results:
What does this p-value mean?

#### Options:
- **A.** The probability of observing a z-value \( < 2.17 \) is equal to the p-value, if \( \mu = 90 \).
- **B.** The probability of observing a z-value \( > 2.17 \) is equal to the p-value, if \( \mu > 90 \).
- **C.** The probability of observing a z-value \( > 2.17 \) is equal to the p-value, if \( \mu = 90 \).
- **D.** The probability of observing a z-value \( < 2.17 \) is equal to the p-value, if \( \mu > 90 \).

#### Correct Answer:
- **C.** The probability of observing a z-value \( > 2.17 \) is equal to the p-value, if \( \mu = 90 \).

This means that there is a 1.5% chance of observing a test statistic as extreme as 2.17 or more extreme in the direction of the alternative hypothesis, assuming the null hypothesis is true.
Transcribed Image Text:### Hypothesis Testing Example In a test of \( H_0: \mu = 90 \) against \( H_a: \mu > 90 \), the sample data yielded the test statistic \( z = 2.17 \). Find and interpret the p-value for the test. #### Instructions: Click the icon to view a table of standard normal values. #### Calculation of p-value: The p-value is \( p = 0.015 \). (Round to three decimal places as needed.) ### Interpretation of Results: What does this p-value mean? #### Options: - **A.** The probability of observing a z-value \( < 2.17 \) is equal to the p-value, if \( \mu = 90 \). - **B.** The probability of observing a z-value \( > 2.17 \) is equal to the p-value, if \( \mu > 90 \). - **C.** The probability of observing a z-value \( > 2.17 \) is equal to the p-value, if \( \mu = 90 \). - **D.** The probability of observing a z-value \( < 2.17 \) is equal to the p-value, if \( \mu > 90 \). #### Correct Answer: - **C.** The probability of observing a z-value \( > 2.17 \) is equal to the p-value, if \( \mu = 90 \). This means that there is a 1.5% chance of observing a test statistic as extreme as 2.17 or more extreme in the direction of the alternative hypothesis, assuming the null hypothesis is true.
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