Part 2 of 3 (b) Estimate the sample size needed if no estimate of p is available. A sample of children aged 8-10 living in New York is needed to obtain a 95% confidence interval with a margin of error of 0.04 when no estimate of p is available.
Part 2 of 3 (b) Estimate the sample size needed if no estimate of p is available. A sample of children aged 8-10 living in New York is needed to obtain a 95% confidence interval with a margin of error of 0.04 when no estimate of p is available.
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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help woth part 2
![### Confidence Interval Calculation for Proportion of Children Owning a Smartphone
**Scenario:**
A sociologist wants to construct a 95% confidence interval for the proportion of children aged 8-10 living in New York who own a smartphone.
#### Part 1:
(a) A survey by the National Consumers League estimated the nationwide proportion to be 0.38. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.04?
**Solution:**
> A sample of **566** children aged 8-10 living in New York is needed to obtain a 95% confidence interval with a margin of error of 0.04 using the estimate 0.38 for \( p \).
#### Part 2:
(b) Estimate the sample size needed if no estimate of \( p \) is available.
**Solution:**
> A sample of [ ] children aged 8-10 living in New York is needed to obtain a 95% confidence interval with a margin of error of 0.04 when no estimate of \( p \) is available.
**Progress Indicator:**
There is a progress bar displaying that the task is 1/3 complete, showing that the user is on the first part of a three-part exercise.
#### Notes:
- **Graphical Elements:** There are no graphs or diagrams in this image.
- **Interactive Elements:**
- Text input box for entering the sample size in part (b).
- "Check" button to verify the answer.
- "Skip Part," "Save For Later," and "Submit Assignment" options are available.
**Rights and Credits:**
This content is © 2023 McGraw Hill LLC. All rights reserved.
**Additional Tips for Students:**
- When no estimate of \( p \) is available, use 0.5 for \( p \) in the sample size calculation as it maximizes the required sample size and provides a conservative estimate.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29a07bd8-eb1c-498d-b0a8-9eb9d6fddf09%2F7cc71f4c-8613-4ed4-92ad-5dd8ec77fa6d%2Fdxuqsy6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Confidence Interval Calculation for Proportion of Children Owning a Smartphone
**Scenario:**
A sociologist wants to construct a 95% confidence interval for the proportion of children aged 8-10 living in New York who own a smartphone.
#### Part 1:
(a) A survey by the National Consumers League estimated the nationwide proportion to be 0.38. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.04?
**Solution:**
> A sample of **566** children aged 8-10 living in New York is needed to obtain a 95% confidence interval with a margin of error of 0.04 using the estimate 0.38 for \( p \).
#### Part 2:
(b) Estimate the sample size needed if no estimate of \( p \) is available.
**Solution:**
> A sample of [ ] children aged 8-10 living in New York is needed to obtain a 95% confidence interval with a margin of error of 0.04 when no estimate of \( p \) is available.
**Progress Indicator:**
There is a progress bar displaying that the task is 1/3 complete, showing that the user is on the first part of a three-part exercise.
#### Notes:
- **Graphical Elements:** There are no graphs or diagrams in this image.
- **Interactive Elements:**
- Text input box for entering the sample size in part (b).
- "Check" button to verify the answer.
- "Skip Part," "Save For Later," and "Submit Assignment" options are available.
**Rights and Credits:**
This content is © 2023 McGraw Hill LLC. All rights reserved.
**Additional Tips for Students:**
- When no estimate of \( p \) is available, use 0.5 for \( p \) in the sample size calculation as it maximizes the required sample size and provides a conservative estimate.
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