"hat is the confidence level of each of the following confidence intervals for u? Complete parts a throughe. Click the icon to view the table of normal curve areas. -x+1.645 90 % (Round to two decimal places as needed.) -x+2.575 99 % (Round to two decimal places as needed.) 1. x±1.282 80 % (Round to two decimal places as needed.) e. x+0.99 % (Round to two decimal places as needed.)

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### Understanding Confidence Intervals

Confidence intervals are a range of values, derived from a dataset, that are used to estimate the true value of a population parameter. They give an estimated range believed to contain the parameter with a specified level of confidence, usually 90%, 95%, or 99%. Here, we are tasked with determining the confidence levels for given confidence intervals.

Please review the following detailed equations and their associated confidence levels:

**a.** \( \bar{x} \pm 1.645 \left( \frac{\sigma}{\sqrt{n}} \right) \)
- 90% (Round to two decimal places as needed.)

**b.** \( \bar{x} \pm 2.575 \left( \frac{\sigma}{\sqrt{n}} \right) \)
- 99% (Round to two decimal places as needed.)

**c.** \( \bar{x} \pm 1.282 \left( \frac{\sigma}{\sqrt{n}} \right) \)
- 80% (Round to two decimal places as needed.)

**d.** \( \bar{x} \pm 0.99 \left( \frac{\sigma}{\sqrt{n}} \right) \)
- __.__ % (Round to two decimal places as needed.)

To solve part **d**:
We must determine the confidence level corresponding to the critical value \( Z = 0.99 \).

### Explanation of Symbols:

- \( \bar{x} \): Sample mean
- \( \sigma \): Population standard deviation
- \( n \): Sample size
- \( \sqrt{n} \): Square root of the sample size

### Using the Table of Normal Curve Areas:
Refer to a Z-table or standard normal distribution table to determine the exact confidence levels:
- 1.645 corresponds to approximately 90%.
- 2.575 corresponds to approximately 99%.
- 1.282 corresponds to approximately 80%.
- 0.99, using the Z-table, corresponds to approximately __.__%.

### Interactive Tool:
Click the icon to view the table of normal curve areas. Use this to match the Z-values to their corresponding percentage areas under the curve, thus helping to understand the confidence levels.

By using these Z-values, you will be able to construct confidence intervals for various levels of confidence, subsequently ensuring the accuracy of population parameter estimations from sample data.
   
Note:
Transcribed Image Text:### Understanding Confidence Intervals Confidence intervals are a range of values, derived from a dataset, that are used to estimate the true value of a population parameter. They give an estimated range believed to contain the parameter with a specified level of confidence, usually 90%, 95%, or 99%. Here, we are tasked with determining the confidence levels for given confidence intervals. Please review the following detailed equations and their associated confidence levels: **a.** \( \bar{x} \pm 1.645 \left( \frac{\sigma}{\sqrt{n}} \right) \) - 90% (Round to two decimal places as needed.) **b.** \( \bar{x} \pm 2.575 \left( \frac{\sigma}{\sqrt{n}} \right) \) - 99% (Round to two decimal places as needed.) **c.** \( \bar{x} \pm 1.282 \left( \frac{\sigma}{\sqrt{n}} \right) \) - 80% (Round to two decimal places as needed.) **d.** \( \bar{x} \pm 0.99 \left( \frac{\sigma}{\sqrt{n}} \right) \) - __.__ % (Round to two decimal places as needed.) To solve part **d**: We must determine the confidence level corresponding to the critical value \( Z = 0.99 \). ### Explanation of Symbols: - \( \bar{x} \): Sample mean - \( \sigma \): Population standard deviation - \( n \): Sample size - \( \sqrt{n} \): Square root of the sample size ### Using the Table of Normal Curve Areas: Refer to a Z-table or standard normal distribution table to determine the exact confidence levels: - 1.645 corresponds to approximately 90%. - 2.575 corresponds to approximately 99%. - 1.282 corresponds to approximately 80%. - 0.99, using the Z-table, corresponds to approximately __.__%. ### Interactive Tool: Click the icon to view the table of normal curve areas. Use this to match the Z-values to their corresponding percentage areas under the curve, thus helping to understand the confidence levels. By using these Z-values, you will be able to construct confidence intervals for various levels of confidence, subsequently ensuring the accuracy of population parameter estimations from sample data. Note:
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