Question #7 ### Statistical Confidence and Sample SizeA doctor aims to estimate the mean HDL cholesterol of all 20- to 29-year-old females. The goal is to determine how many subjects are necessary to estimate the mean HDL cholesterol within 2 points with a 99% confidence level, assuming the standard deviation (\(s\)) is 12.9 based on previous studies. The doctor also considers a 90% confidence level. How does adjusting the confidence level impact the required sample size?**Sample Size Calculation:**- **99% confidence level requires:** [ ] subjects. *(Round up to the nearest subject.)*- **90% confidence level requires:** [ ] subjects. *(Round up to the nearest subject.)***Effect of Confidence Level on Sample Size:**- **A.** Decreasing the confidence level decreases the sample size needed.- **B.** The sample size is the same for all levels of confidence.- **C.** Decreasing the confidence level increases the sample size needed.### Partial Critical Value TableThis table provides the critical values (\(z_{\alpha/2}\)) for various confidence levels, which are necessary for calculating sample size:| Level of Confidence, \((1-\alpha) \cdot 100\%\) | Area in Each Tail, \(\alpha/2\) | Critical Value, \(z_{\alpha/2}\) ||---------------------------------------------------|---------------------------------|---------------------------------|| 90% | 0.05 | 1.645 || 95% | 0.025 | 1.96 || 99% | 0.005 | 2.575 |### Understanding the Table:- The **level of confidence** refers to how certain we are that the true parameter lies within the confidence interval.- The **critical value** \(z_{\alpha/2}\) corresponds to the chosen confidence level, impacting the margin of error and the sample size needed for a given precision.

We want to find the sample size

A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 2 points with 99% confidence assuming s= 12.9 based on earlier studies? Suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size required? E Click the icon to view a partial table of critical values. A 99% confidence level requires subjects. (Round up to the nearest subject.) Partial critical value table A 90% confidence level requires subjects. (Round up to the nearest subject.) Critical Value, za/2 Level of Confidence, (1-a)• 100% Area in Each Tail, 2 How does the decrease in confidence affect the sample size required? 90% 95% 0.05 1.645 1.96 2.575 O A. Decreasing the confidence level decreases the sample size needed. 0.025 O B. The sample size is the same for all levels of confidence. 99% 0.005 OC. Decreasing the confidence level increases the sample size needed.

A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 2 points with 99% confidence assuming s= 12.9 based on earlier studies? Suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size required? E Click the icon to view a partial table of critical values. A 99% confidence level requires subjects. (Round up to the nearest subject.) Partial critical value table A 90% confidence level requires subjects. (Round up to the nearest subject.) Critical Value, za/2 Level of Confidence, (1-a)• 100% Area in Each Tail, 2 How does the decrease in confidence affect the sample size required? 90% 95% 0.05 1.645 1.96 2.575 O A. Decreasing the confidence level decreases the sample size needed. 0.025 O B. The sample size is the same for all levels of confidence. 99% 0.005 OC. Decreasing the confidence level increases the sample size needed.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question #7

### Statistical Confidence and Sample Size

A doctor aims to estimate the mean HDL cholesterol of all 20- to 29-year-old females. The goal is to determine how many subjects are necessary to estimate the mean HDL cholesterol within 2 points with a 99% confidence level, assuming the standard deviation (\(s\)) is 12.9 based on previous studies. The doctor also considers a 90% confidence level. How does adjusting the confidence level impact the required sample size?

**Sample Size Calculation:**
- **99% confidence level requires:** [ ] subjects. *(Round up to the nearest subject.)*
- **90% confidence level requires:** [ ] subjects. *(Round up to the nearest subject.)*

**Effect of Confidence Level on Sample Size:**
- **A.** Decreasing the confidence level decreases the sample size needed.
- **B.** The sample size is the same for all levels of confidence.
- **C.** Decreasing the confidence level increases the sample size needed.

### Partial Critical Value Table

This table provides the critical values (\(z_{\alpha/2}\)) for various confidence levels, which are necessary for calculating sample size:

| Level of Confidence, \((1-\alpha) \cdot 100\%\) | Area in Each Tail, \(\alpha/2\) | Critical Value, \(z_{\alpha/2}\) |
|---------------------------------------------------|---------------------------------|---------------------------------|
| 90% | 0.05 | 1.645 |
| 95% | 0.025 | 1.96 |
| 99% | 0.005 | 2.575 |

### Understanding the Table:
- The **level of confidence** refers to how certain we are that the true parameter lies within the confidence interval.
- The **critical value** \(z_{\alpha/2}\) corresponds to the chosen confidence level, impacting the margin of error and the sample size needed for a given precision.

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