If sigma = 0.01
, what is the critical value? If there is more than one, separate it out by comma.

To find the critical value when \( \sigma = 0.01 \), we first need to know more context—specifically, whether you are referring to:

1. **A z-distribution (standard normal distribution)**: In this case, \( \sigma \) refers to the significance level (often called alpha, \( \alpha \)) of a hypothesis test.
2. **A t-distribution**: In this case, it would depend on the degrees of freedom.
3. **Chi-square, F-distribution**, or others.

Assuming you mean a **z-distribution** (common in hypothesis tests like a one-sample z-test), the critical value for \( \sigma = 0.01 \) corresponds to a confidence level of \( 99\% \) (since \( 1 - 0.01 = 0.99 \)).

### For a two-tailed test:
- We are interested in the critical values that leave 0.01/2 = 0.005 in each tail.
- Using a z-distribution table, the critical values are approximately \( \pm 2.576 \).

Thus, the critical values for a two-tailed z-test at \( \sigma = 0.01 \) are:

\[
\text{Critical values} = -2.576, +2.576
\]

### For a one-tailed test:
- If you're performing a one-tailed test, the critical value for \( \sigma = 0.01 \) corresponds to \( z = 2.326 \) for the upper tail and \( z = -2.326 \) for the lower tail.

Would you like to dive into more details on z-scores or expand on a different distribution?

Here are 5 relative questions you might consider:
1. How do critical values change with different significance levels (\( \sigma \))?
2. How do critical values differ between one-tailed and two-tailed tests?
3. What is the role of degrees of freedom in determining critical values for the t-distribution?
4. How do you calculate p-values using critical values?
5. What is the relationship between confidence intervals and critical values?

**Tip:** In hypothesis testing, always double-check if you are dealing with a one-tailed or two-tailed test, as this significantly impacts your critical values.

If sigma = 0.01, what is the critical value? If there is more than one, separate it out by comma.

Discover how to find critical values for a significance level (sigma) of 0.01 in both one-tailed and two-tailed hypothesis tests. Explore key concepts in Z-distribution and hypothesis testing with step-by-step solutions. Suitable for undergraduate students in statistics.

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