(a) How many subjects are needed to estimate the mean number of books read the previous year within six books with 90% confidence? This 90% confidence level requires subjects. (Round up to the nearest subject.)
(a) How many subjects are needed to estimate the mean number of books read the previous year within six books with 90% confidence? This 90% confidence level requires subjects. (Round up to the nearest subject.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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![**Transcription with Details for Educational Purposes**
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People were polled on how many books they read the previous year. Initial survey results indicate that \( s = 13.3 \) books. Complete parts (a) through (d) below.
\[ \text{(a) How many subjects are needed to estimate the mean number of books read the previous year within six books with 90% confidence?} \]
This 90% confidence level requires \[ \_\_\_ \] subjects. (Round up to the nearest subject.)
**Partial Critical Value Table:**
| 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 |
Below the table, there are buttons labeled "Print" and "Done."
---
**Explanation of the Table:**
The table provides critical values \(z_{\alpha/2}\) for different levels of confidence in a normal distribution. For a given confidence level, it shows the area in each tail (\(\alpha/2\)), which is used to find the critical value needed to calculate confidence intervals.
- **90% Confidence Level:** The critical value is 1.645, corresponding to an area of 0.05 in each tail.
- **95% Confidence Level:** The critical value is 1.96, corresponding to an area of 0.025 in each tail.
- **99% Confidence Level:** The critical value is 2.575, corresponding to an area of 0.005 in each tail.
These critical values are instrumental in determining the sample size required for the desired confidence level when estimating population means.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca98936e-33c7-4402-95ae-aeafe8e3f8b8%2F488659f2-5f1a-4d30-a04b-3d2b7be936db%2Fnl9g9ng_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription with Details for Educational Purposes**
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People were polled on how many books they read the previous year. Initial survey results indicate that \( s = 13.3 \) books. Complete parts (a) through (d) below.
\[ \text{(a) How many subjects are needed to estimate the mean number of books read the previous year within six books with 90% confidence?} \]
This 90% confidence level requires \[ \_\_\_ \] subjects. (Round up to the nearest subject.)
**Partial Critical Value Table:**
| 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 |
Below the table, there are buttons labeled "Print" and "Done."
---
**Explanation of the Table:**
The table provides critical values \(z_{\alpha/2}\) for different levels of confidence in a normal distribution. For a given confidence level, it shows the area in each tail (\(\alpha/2\)), which is used to find the critical value needed to calculate confidence intervals.
- **90% Confidence Level:** The critical value is 1.645, corresponding to an area of 0.05 in each tail.
- **95% Confidence Level:** The critical value is 1.96, corresponding to an area of 0.025 in each tail.
- **99% Confidence Level:** The critical value is 2.575, corresponding to an area of 0.005 in each tail.
These critical values are instrumental in determining the sample size required for the desired confidence level when estimating population means.
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