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= 11.6 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. Partial critical value table A 99% confidence level requires 224 subjects. (Round up to the nearest subject.) 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, 0.05 90% 95% 99% 1.645 0.025 1.96 0.005 2.575 Print Done
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= 11.6 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. Partial critical value table A 99% confidence level requires 224 subjects. (Round up to the nearest subject.) 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, 0.05 90% 95% 99% 1.645 0.025 1.96 0.005 2.575 Print Done
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 Part 2
![**Educational Content: Estimating Sample Size for Statistical Confidence**
A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. The task is to determine how many subjects are needed to estimate the mean HDL cholesterol within 2 points, with 99% confidence, assuming a standard deviation \( s = 11.6 \) based on earlier studies. Additionally, consider how the sample size requirement is affected by decreasing the confidence level to 90%.
**Sample Size Requirements:**
- A 99% confidence level requires **224 subjects.** (Round up to the nearest subject.)
- A 90% confidence level requires **[Input Required]** subjects. (Round up to the nearest subject.)
**Partial Critical Value Table:**
This table provides information about different confidence levels and their corresponding critical values. It is used to determine sample sizes for different confidence intervals.
| Level of Confidence | 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 |
This table helps in understanding the impact of confidence levels on sample size requirements. With higher confidence levels, larger critical values necessitate larger sample sizes to achieve the same precision in estimates.
**Conclusion:**
Decreasing the confidence level from 99% to 90% reduces the sample size needed. This illustrates the trade-off between the precision of the estimate and the confidence level.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3687cbc-fe37-486e-87e6-a5fec1076243%2Fea6a3d53-1e68-4d8a-80e2-e4dcea64d4f5%2Fijsln2b_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Content: Estimating Sample Size for Statistical Confidence**
A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. The task is to determine how many subjects are needed to estimate the mean HDL cholesterol within 2 points, with 99% confidence, assuming a standard deviation \( s = 11.6 \) based on earlier studies. Additionally, consider how the sample size requirement is affected by decreasing the confidence level to 90%.
**Sample Size Requirements:**
- A 99% confidence level requires **224 subjects.** (Round up to the nearest subject.)
- A 90% confidence level requires **[Input Required]** subjects. (Round up to the nearest subject.)
**Partial Critical Value Table:**
This table provides information about different confidence levels and their corresponding critical values. It is used to determine sample sizes for different confidence intervals.
| Level of Confidence | 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 |
This table helps in understanding the impact of confidence levels on sample size requirements. With higher confidence levels, larger critical values necessitate larger sample sizes to achieve the same precision in estimates.
**Conclusion:**
Decreasing the confidence level from 99% to 90% reduces the sample size needed. This illustrates the trade-off between the precision of the estimate and the confidence level.
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