The proportion of students who pass the Virginia 8th grade SOL test before 2005 on the first try was greater than 84%. If a new random sample of 1250 test scores is collected to determine if the pass rate is still above 84% and 1075 students passed, what is the P-value and decision of this test? Test at the 0.05 level of significance. Assume all conditions are met and use the one sample Z-test on the proportion. P-value = 0.9731. Reject the null hypothesis. P-value = 0.9731. Do not reject the null hypothesis. P-value = 0.0269. Do not reject the null hypothesis. P-value = 0.0269. Reject the null hypothesis.

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The provided text outlines a statistical problem involving hypothesis testing:

The problem states that the proportion of students who passed the Virginia 8th grade SOL test before 2005 on their first try was greater than 84%. A new random sample of 1250 test scores is used to determine if the pass rate still exceeds 84%, with 1075 students passing.

The task is to find the P-value and make a decision based on a one-sample Z-test for proportions at the 0.05 level of significance. All conditions for the test are assumed to be met.

Four options are given regarding the P-value and the corresponding decision:

1. **P-value = 0.9731. Reject the null hypothesis.**
2. **P-value = 0.9731. Do not reject the null hypothesis.**
3. **P-value = 0.0269. Do not reject the null hypothesis.**
4. **P-value = 0.0269. Reject the null hypothesis.**

The correct choice is highlighted, indicating that:

- **P-value = 0.9731. Do not reject the null hypothesis.**
Transcribed Image Text:The provided text outlines a statistical problem involving hypothesis testing: The problem states that the proportion of students who passed the Virginia 8th grade SOL test before 2005 on their first try was greater than 84%. A new random sample of 1250 test scores is used to determine if the pass rate still exceeds 84%, with 1075 students passing. The task is to find the P-value and make a decision based on a one-sample Z-test for proportions at the 0.05 level of significance. All conditions for the test are assumed to be met. Four options are given regarding the P-value and the corresponding decision: 1. **P-value = 0.9731. Reject the null hypothesis.** 2. **P-value = 0.9731. Do not reject the null hypothesis.** 3. **P-value = 0.0269. Do not reject the null hypothesis.** 4. **P-value = 0.0269. Reject the null hypothesis.** The correct choice is highlighted, indicating that: - **P-value = 0.9731. Do not reject the null hypothesis.**
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