Find the critical value, z α 2 z_{\frac{\alpha}{2}} , for a 80% confidence interval.

Here, we're asked to find the critical value, z alpha over 2, for an 80% confidence interval. So the first thing we want to do here is find alpha over 2. So this is going to be 1 minus c, our confidence level, over 2. Now in this case, since we have this confidence level of 80%, this is 1 minus 0.8 over 2, which ultimately gives us an alpha over 2 value of 0.1. Now remember that from this point, there are 2 ways that you could go about this. You could look this value up in a z table or you could use your calculator. Now if you are using your calculator, remember that this is the area underneath one of our tails here. So if you're looking for this z alpha over 2 value, the positive one on the other side here, you also need to include all of this area here. So if this area is 0.1, that's what we just found, and this area here is our confidence level, 0.8, that means when you type this into your calculator, you need to note that your area here is 0 point 9. That's these two values added together because, remember, this is the total area to the left of your boundary. Now if you are not using a calculator, you can just look up this 0.1 in the body of your z table, and it will give you the negative version of your critical value. Now either way that you choose to do this, you should end up getting an answer here that z alpha over 2 is equal to 1.282 and this is our final answer. Feel free to let us know if you have any questions, and let's keep going.

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1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

7. Sampling Distributions & Confidence Intervals: Mean

Introduction to Confidence Intervals

Statistics

7. Sampling Distributions & Confidence Intervals: Mean

Introduction to Confidence Intervals

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Multiple Choice

Find the critical value, $z sub alpha over 2$ , for a 80% confidence interval.

0.10

1.282

0.40

0.90

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Verified step by step guidance

Understand that the critical value, z_{\frac{\alpha}{2}}, is used in constructing confidence intervals for a population mean when the population standard deviation is known.

Recognize that for a confidence level of 80%, the significance level $ \alpha $ is 0.20, because $ \alpha = 1 - \text{confidence level} $.

Calculate $ \frac{\alpha}{2} $ to find the tail probability for the critical value. For $ \alpha = 0.20 $, $ \frac{\alpha}{2} = 0.10 $.

Use the standard normal distribution table or a calculator to find the z-score that corresponds to the cumulative probability of 0.90 (since 1 - 0.10 = 0.90). This z-score is the critical value, z_{\frac{\alpha}{2}}.

Verify the critical value by checking the z-score table or using statistical software to ensure it matches the expected value for a 80% confidence interval.