People were polled on how many books they read the previous year. Initial survey results indicate that s= 19.9 books. Complete parts (a) through (d) below. A Click the icon to view a partial table of critical values. (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 (b) How many subjects are needed to estimate the mean number of books read the previous year within three books with 90% confidence? This 90% confidence level requires subjects. (Round up to the nearest subject.) (c) What effect does doubling the required accuracy have on the sample size? Level of Confidence, (1-a)• 100% Critical Value, Zu/2 Area in Each Tail, O A. Doubling the required accuracy nearly quadruples the sample size. O B. Doubling the required accuracy nearly doubles the sample size. OC. Doubling the required accuracy nearly halves the sample size. O D. Doubling the required accuracy nearly quarters the sample size. 0.05 0.025 1.645 90% 95% 1.96 99% 0.005 2.575 Print Done (d) How many subjects are needed to estimate the mean number of books read the previous year within six books with 99% confidence?
People were polled on how many books they read the previous year. Initial survey results indicate that s= 19.9 books. Complete parts (a) through (d) below. A Click the icon to view a partial table of critical values. (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 (b) How many subjects are needed to estimate the mean number of books read the previous year within three books with 90% confidence? This 90% confidence level requires subjects. (Round up to the nearest subject.) (c) What effect does doubling the required accuracy have on the sample size? Level of Confidence, (1-a)• 100% Critical Value, Zu/2 Area in Each Tail, O A. Doubling the required accuracy nearly quadruples the sample size. O B. Doubling the required accuracy nearly doubles the sample size. OC. Doubling the required accuracy nearly halves the sample size. O D. Doubling the required accuracy nearly quarters the sample size. 0.05 0.025 1.645 90% 95% 1.96 99% 0.005 2.575 Print Done (d) How many subjects are needed to estimate the mean number of books read the previous year within six books with 99% confidence?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 25SGR
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Question
![**Estimating Sample Sizes for Book Reading Surveys**
**Context:**
People were surveyed on how many books they read the previous year. Initial survey results indicate that the sample standard deviation \( s = 19.9 \) books. Complete parts (a) through (d) below.
---
**Sample Size Calculations:**
(a) **Estimating with 90% Confidence:**
- 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.)*
(b) **Estimating with Increased Accuracy:**
- How many subjects are needed to estimate the mean number of books read the previous year within three books with 90% confidence?
- This 90% confidence level requires [ ] subjects. *(Round up to the nearest subject.)*
**Effect of Doubling the Required Accuracy:**
(c) What effect does doubling the required accuracy have on the sample size?
- A. Doubling the required accuracy nearly quadruples the sample size.
- B. Doubling the required accuracy nearly doubles the sample size.
- C. Doubling the required accuracy nearly halves the sample size.
- D. Doubling the required accuracy nearly quarters the sample size.
**Higher Confidence Level Requirement:**
(d) How many subjects are needed to estimate the mean number of books read the previous year within six books with 99% confidence?
- This 99% confidence level requires [ ] subjects. *(Round up to the nearest subject.)*
**Analyzing Confidence Levels:**
Compare this result to part (a). How does increasing the level of confidence in the estimate affect sample size? Why is this reasonable?
- A. Increasing the level of confidence decreases the sample size required. For a fixed margin of error, greater confidence can be achieved with a smaller sample size.
- B. Increasing the level of confidence increases the sample size required. For a fixed margin of error, greater confidence can be achieved with a smaller sample size.
- C. Increasing the level of confidence increases the sample size required. For a fixed margin of error, greater confidence can be achieved with a larger sample size.
- D. Increasing the level of confidence decreases the sample size required. For a fixed margin of error, greater confidence can be achieved with a larger sample size.
---
**Partial Critical Value Table:**
- **Level of Confidence**: 90%,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa2a79f3c-9d5f-475d-8512-37c872933c1c%2Fd68b24e8-b8eb-4722-8cd0-533a2175eae9%2Fd3pui5i_processed.png&w=3840&q=75)
Transcribed Image Text:**Estimating Sample Sizes for Book Reading Surveys**
**Context:**
People were surveyed on how many books they read the previous year. Initial survey results indicate that the sample standard deviation \( s = 19.9 \) books. Complete parts (a) through (d) below.
---
**Sample Size Calculations:**
(a) **Estimating with 90% Confidence:**
- 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.)*
(b) **Estimating with Increased Accuracy:**
- How many subjects are needed to estimate the mean number of books read the previous year within three books with 90% confidence?
- This 90% confidence level requires [ ] subjects. *(Round up to the nearest subject.)*
**Effect of Doubling the Required Accuracy:**
(c) What effect does doubling the required accuracy have on the sample size?
- A. Doubling the required accuracy nearly quadruples the sample size.
- B. Doubling the required accuracy nearly doubles the sample size.
- C. Doubling the required accuracy nearly halves the sample size.
- D. Doubling the required accuracy nearly quarters the sample size.
**Higher Confidence Level Requirement:**
(d) How many subjects are needed to estimate the mean number of books read the previous year within six books with 99% confidence?
- This 99% confidence level requires [ ] subjects. *(Round up to the nearest subject.)*
**Analyzing Confidence Levels:**
Compare this result to part (a). How does increasing the level of confidence in the estimate affect sample size? Why is this reasonable?
- A. Increasing the level of confidence decreases the sample size required. For a fixed margin of error, greater confidence can be achieved with a smaller sample size.
- B. Increasing the level of confidence increases the sample size required. For a fixed margin of error, greater confidence can be achieved with a smaller sample size.
- C. Increasing the level of confidence increases the sample size required. For a fixed margin of error, greater confidence can be achieved with a larger sample size.
- D. Increasing the level of confidence decreases the sample size required. For a fixed margin of error, greater confidence can be achieved with a larger sample size.
---
**Partial Critical Value Table:**
- **Level of Confidence**: 90%,
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