ind the critical​ value(s) for a​ left-tailed z-test with alphaequals0.01. Include a graph with your answer.
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Part 1
The critical​ value(s) is(are) 
  
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The critical value for the left-tailed \( z \)-test with \( \alpha = 0.01 \) is \( z = -2.33 \). The shaded area on the left of the critical value in the graph represents the rejection region for the test, corresponding to 1% of the total area under the curve.

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Here are five related questions for further exploration:
1. How do you calculate the critical value for a right-tailed test?
2. What is the critical value for a two-tailed \( z \)-test with \( \alpha = 0.05 \)?
3. How do you interpret a \( z \)-score in hypothesis testing?
4. How does the rejection region change with different values of \( \alpha \)?
5. What is the difference between one-tailed and two-tailed tests in hypothesis testing?

**Tip:** When conducting hypothesis tests, always ensure that the significance level \( \alpha \) matches the context of your analysis, as it directly affects the rejection region.

Find the critical​ value(s) for a​ left-tailed z-test with alpha equals 0.01. Include a graph with your answer.

Determine the critical value for a left-tailed z-test with a significance level of 0.01. Understand the rejection region and the role of the standard normal distribution. Includes step-by-step solution and graph.

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