A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 2

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A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. The value of the test statistic and its associated p-value are ________

**Hypothesis Testing Example for University Honors Program**

A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. The value of the test statistic and its associated *p*-value are __________.

**Multiple Choice:**

1. \( t_{199} = -1.77 \) and *p*-value = 0.0385
2. \( t_{199} = -1.77 \) and *p*-value = 0.0768
3. \( z = -1.77 \) and *p*-value = 0.0768
4. \( z = -1.77 \) and *p*-value = 0.0385

**Explanation:**

This is a hypothesis testing problem where we are given a sample of 200 graduates, out of which 30 have a GPA of 3.00 or below. We need to determine the test statistic and *p*-value for the hypothesis that the proportion (\( p \)) of students with a GPA of 3.00 or below is less than 0.20. 

Students should select the correct test statistic and *p*-value from the options provided. The test statistic could either be a *t*-value or a *z*-value, depending on the sample size and assumptions.
Transcribed Image Text:**Hypothesis Testing Example for University Honors Program** A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. The value of the test statistic and its associated *p*-value are __________. **Multiple Choice:** 1. \( t_{199} = -1.77 \) and *p*-value = 0.0385 2. \( t_{199} = -1.77 \) and *p*-value = 0.0768 3. \( z = -1.77 \) and *p*-value = 0.0768 4. \( z = -1.77 \) and *p*-value = 0.0385 **Explanation:** This is a hypothesis testing problem where we are given a sample of 200 graduates, out of which 30 have a GPA of 3.00 or below. We need to determine the test statistic and *p*-value for the hypothesis that the proportion (\( p \)) of students with a GPA of 3.00 or below is less than 0.20. Students should select the correct test statistic and *p*-value from the options provided. The test statistic could either be a *t*-value or a *z*-value, depending on the sample size and assumptions.
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