A local school board wants to determine if the proportion of households in the district that would support starting the school year a week earlier has changed from the previous year. Last year, the school board determined that 65% of households supported starting school earlier. They ask a random sample of 100 households this year, and 70% state they would support starting the school year earlier. The *P*-value for the test of the hypotheses, , is 0.29. What is the correct interpretation of this value?

Only 29% of households in this sample approve of starting school earlier.

Assuming 65% of households would support starting school earlier, there is a 0.29 probability of getting a sample proportion of 0.70 or more different from 0.65.

Assuming 65% or more households would support starting school earlier, there is a 0.29 probability of getting a sample proportion of 0.70 or more different from 0.65.

Assuming this sample was collected correctly, the probability of getting 70 households out of 100 that would support starting school earlier is 0.29 if 65% of households truly support starting school earlier.

The correct interpretation of the *P*-value is:

**"Assuming 65% of households would support starting school earlier, there is a 0.29 probability of getting a sample proportion of 0.70 or more different from 0.65."**

This is because a *P*-value measures the probability of observing a result as extreme or more extreme than the one found in the sample, assuming that the null hypothesis (in this case, that 65% of households still support starting school earlier) is true.

To clarify:

- The null hypothesis is that the true proportion of households that support starting school earlier is still 65%.
- A *P*-value of 0.29 indicates that there is a 29% chance of getting a sample proportion of 70% (0.70) or more different from 65% (0.65) if the true proportion is indeed 65%.
- Since this *P*-value is relatively large, it suggests that there is no strong evidence to reject the null hypothesis.

Would you like more details on hypothesis testing or the interpretation of *P*-values?

Here are 5 questions related to this topic:

1. What are the null and alternative hypotheses in hypothesis testing?
2. How do you calculate a *P*-value for a proportion hypothesis test?
3. What is the significance level, and how does it relate to the *P*-value?
4. What does it mean if the *P*-value is smaller than the significance level?
5. How would you compute a confidence interval for the proportion of households supporting starting school earlier?

**Tip:** A *P*-value only tells you the probability under the null hypothesis, not whether the null hypothesis is true.

A local school board wants to determine if the proportion of households in the district that would support starting the school year a week earlier has changed from the previous year. Last year, the school board determined that 65% of households supported starting school earlier. They ask a random sample of 100 households this year, and 70% state they would support starting the school year earlier. The *P*-value for the test of the hypotheses is 0.29. What is the correct interpretation of this value?

Learn how to interpret the P-value for hypothesis testing regarding the proportion of households supporting an earlier school start. This example involves a sample size of 100 households and a comparison to the previous year's support rate of 65%. Suitable for high school and college-level students interested in statistics and hypothesis testing.

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