(a) How many subjects are needed to estimate the mean number of books read the previous year within four books with 95% confidence? This 95% confidence level requires subjects. (Round up to the nearest subject.) (b) How many subjects are needed to estimate the mean number of books read the previous year within two books with 95% confidence? This 95% confidence level requires subjects. (Round up to the nearest subject.) (c) What effect does doubling the required accuracy have on the sample size? O A. Doubling the required accuracy nearly halves the sample size. O B. Doubling the required accuracy nearly doubles the sample size. OC. Doubling the required accuracy nearly quadruples the sample size. O D. Doubling the required accuracy nearly quarters the sample size. (d) How many subjects are needed to estimate the mean number of books read the previous year within four books with 99% confidence? This 99% 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 four books with 95% confidence? This 95% confidence level requires subjects. (Round up to the nearest subject.) (b) How many subjects are needed to estimate the mean number of books read the previous year within two books with 95% confidence? This 95% confidence level requires subjects. (Round up to the nearest subject.) (c) What effect does doubling the required accuracy have on the sample size? O A. Doubling the required accuracy nearly halves the sample size. O B. Doubling the required accuracy nearly doubles the sample size. OC. Doubling the required accuracy nearly quadruples the sample size. O D. Doubling the required accuracy nearly quarters the sample size. (d) How many subjects are needed to estimate the mean number of books read the previous year within four books with 99% confidence? This 99% 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
Problem 1P
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![### Understanding Sample Size Requirements for Estimating the Mean Number of Books Read
A survey was conducted to determine the number of books read by people in the previous year. The initial survey results indicate a standard deviation \( s = 14.6 \) books. Below, we address a series of questions about sample size estimation to achieve certain confidence levels and accuracies.
#### (a) Estimating with 95% Confidence Within Four Books
To determine the number of subjects needed to estimate the mean number of books read within a margin of error of four books and with 95% confidence, a specific calculation is required. The sample size will provide a reliable estimate within the desired accuracy.
**95% Confidence Level Requirement:**
\[ \text{Required Sample Size: } \_\_\_ \text{ subjects} \]
*(Round up to the nearest subject.)*
#### (b) Estimating with 95% Confidence Within Two Books
This scenario inquires about estimating the mean with a tighter accuracy of two books but maintaining the same 95% confidence level. Naturally, achieving this level of precision requires a larger sample size.
**95% Confidence Level Requirement:**
\[ \text{Required Sample Size: } \_\_\_ \text{ subjects} \]
*(Round up to the nearest subject.)*
#### (c) Impact of Doubling Required Accuracy on Sample Size
Exploring how changes in the desired accuracy affect sample size is crucial. Specifically, if the accuracy requirement is doubled, what effect does this have on the sample size needed?
- **A.** Doubling the required accuracy nearly halves the sample size.
- **B.** Doubling the required accuracy nearly doubles the sample size.
- **C.** Doubling the required accuracy nearly quadruples the sample size.
- **D.** Doubling the required accuracy nearly quarters the sample size.
#### (d) Estimating with 99% Confidence Within Four Books
Finally, determining how many subjects are needed when increasing the confidence level to 99% while maintaining an accuracy of four books is key for higher certainty in estimates.
**99% Confidence Level Requirement:**
\[ \text{Required Sample Size: } \_\_\_ \text{ subjects} \]
*(Round up to the nearest subject.)*
These exercises illustrate the relationship and balance between confidence levels, accuracy, and sample sizes in statistical estimations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb0ce43c-1343-4636-bcaf-407be51cc0c4%2Fec48784a-4b81-4b2b-8a22-79eeb55975f8%2Fbkhkarvq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Sample Size Requirements for Estimating the Mean Number of Books Read
A survey was conducted to determine the number of books read by people in the previous year. The initial survey results indicate a standard deviation \( s = 14.6 \) books. Below, we address a series of questions about sample size estimation to achieve certain confidence levels and accuracies.
#### (a) Estimating with 95% Confidence Within Four Books
To determine the number of subjects needed to estimate the mean number of books read within a margin of error of four books and with 95% confidence, a specific calculation is required. The sample size will provide a reliable estimate within the desired accuracy.
**95% Confidence Level Requirement:**
\[ \text{Required Sample Size: } \_\_\_ \text{ subjects} \]
*(Round up to the nearest subject.)*
#### (b) Estimating with 95% Confidence Within Two Books
This scenario inquires about estimating the mean with a tighter accuracy of two books but maintaining the same 95% confidence level. Naturally, achieving this level of precision requires a larger sample size.
**95% Confidence Level Requirement:**
\[ \text{Required Sample Size: } \_\_\_ \text{ subjects} \]
*(Round up to the nearest subject.)*
#### (c) Impact of Doubling Required Accuracy on Sample Size
Exploring how changes in the desired accuracy affect sample size is crucial. Specifically, if the accuracy requirement is doubled, what effect does this have on the sample size needed?
- **A.** Doubling the required accuracy nearly halves the sample size.
- **B.** Doubling the required accuracy nearly doubles the sample size.
- **C.** Doubling the required accuracy nearly quadruples the sample size.
- **D.** Doubling the required accuracy nearly quarters the sample size.
#### (d) Estimating with 99% Confidence Within Four Books
Finally, determining how many subjects are needed when increasing the confidence level to 99% while maintaining an accuracy of four books is key for higher certainty in estimates.
**99% Confidence Level Requirement:**
\[ \text{Required Sample Size: } \_\_\_ \text{ subjects} \]
*(Round up to the nearest subject.)*
These exercises illustrate the relationship and balance between confidence levels, accuracy, and sample sizes in statistical estimations.
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