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.