(d)Find the two critical values. (Round to three or more decimal places.)

For a two-tailed z-test at the 0.05 significance level, the critical values are the z-scores that correspond to the tails of the standard normal distribution, such that the total area in both tails is 0.05. This means each tail will have an area of 0.025.

To find the critical values, we need to determine the z-scores that correspond to the cumulative probabilities of \( 0.025 \) and \( 0.975 \) in the standard normal distribution.

Let’s calculate the two critical values.The two critical values for a two-tailed test at the 0.05 significance level are approximately **-1.960** and **1.960**.

Would you like to proceed with interpreting these results or calculating the p-value? 

Here are some related questions:

1. What does it mean if the test statistic falls between the two critical values?
2. How do you calculate the p-value for a two-tailed test?
3. What conclusion can you draw based on the critical values and the test statistic?
4. What is the rejection region for this hypothesis test?
5. How would the critical values change if the significance level were 0.01?
6. Can you visually represent the critical regions on a standard normal distribution curve?
7. What happens if the test statistic is exactly at one of the critical values?
8. How does increasing the sample size affect the critical values?

**Tip:** Understanding the relationship between the test statistic and critical values helps to make the correct decision in hypothesis testing.

Learn how to find critical values for a two-tailed z-test at the 0.05 significance level. Understand the concept of standard normal distribution, significance levels, and their implications in hypothesis testing. Suitable for undergraduate-level study.

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