Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN: 9780079039897
Author: Carter
Publisher: McGraw Hill
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![**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%,](https://content.bartleby.com/qna-images/question/a2a79f3c-9d5f-475d-8512-37c872933c1c/d68b24e8-b8eb-4722-8cd0-533a2175eae9/d3pui5i_processed.png)
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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