You are conducting a study to see if the proportion of voters who prefer democrats is significantly more than 0.78. Thus you are performing a right-tailed test. Your sample data produce the test statistic z=3.084. Find the p-value accurate to 4 decimal places.

p-value =

To find the p-value for a right-tailed test with a z-score of 3.084, we need to look up the cumulative probability corresponding to this z-score in the standard normal distribution.

The p-value is the area to the right of the z-score, so we will first find the cumulative probability to the left of \( z = 3.084 \) and then subtract it from 1.

Using a standard normal table or a calculator:

- The cumulative probability for \( z = 3.084 \) is approximately 0.9990.

Thus, the p-value is:

\[
\text{p-value} = 1 - 0.9990 = 0.0010
\]

So, the p-value is **0.0010**.

Would you like a further explanation or have any other questions on this topic?

### Related Questions:
1. How do you interpret the p-value in hypothesis testing?
2. What is the significance of a z-test in hypothesis testing?
3. How can you determine the critical value for a right-tailed test?
4. What happens if the p-value is less than the significance level (α)?
5. How does the z-test compare to the t-test?

### Tip:
When conducting hypothesis tests, always check if the sample size is large enough to justify using a z-test, typically \( n > 30 \), or if you are testing proportions, if \( np \) and \( n(1-p) \) are both greater than 5.

You are conducting a study to see if the proportion of voters who prefer democrats is significantly more than 0.78. Thus you are performing a right-tailed test. Your sample data produce the test statistic z=3.084. Find the p-value accurate to 4 decimal places.

Learn how to calculate the p-value for a right-tailed z-test when the test statistic is 3.084. This step-by-step guide explains the process for determining the p-value, including looking up cumulative probabilities in the standard normal distribution. Suitable for students in Grades 11-12.

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