MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question

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.
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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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