Call me: 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: 0/3 Part 1 of 3 (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? 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 using the estimate 0.38 for p. X

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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**Estimation of Sample Size for a 95% Confidence Interval**

**Scenario Description:**

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 of 3**

**Task (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 [  ] 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 \( p \).

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**Instructions for Completing the Task:**

1. **Skip Part**: Click the "Skip Part" button if you want to move on to the next part without completing this section.
2. **Check**: After determining the sample size, enter your answer in the blank provided and click the "Check" button to verify correctness.

**Options Available:**

- **Save For Later**: You can bookmark your current progress by clicking "Save For Later".
- **Submit Assignment**: Click this button to submit your completed assignment once all parts are finished.

---

**Additional Information**:

- **Margin of Error (E)**: The margin of error is the range within which the true proportion is expected to fall. In this task, the margin of error is 0.04.
- **Proportion (p)**: The estimated proportion from the survey is 0.38.
- **Confidence Level**: The confidence level for this interval is 95%.

**Graphical/Diagrammatic Explanation**:

No graphs or diagrams are present in the provided text. Should there be any, they would be explained in detail to assist in understanding the data and the necessary calculations.

For further questions and explanations, references to statistical formulas and methods to calculate sample size can be provided.

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Transcribed Image Text:--- **Estimation of Sample Size for a 95% Confidence Interval** **Scenario Description:** 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 of 3** **Task (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 [ ] 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 \( p \). --- **Instructions for Completing the Task:** 1. **Skip Part**: Click the "Skip Part" button if you want to move on to the next part without completing this section. 2. **Check**: After determining the sample size, enter your answer in the blank provided and click the "Check" button to verify correctness. **Options Available:** - **Save For Later**: You can bookmark your current progress by clicking "Save For Later". - **Submit Assignment**: Click this button to submit your completed assignment once all parts are finished. --- **Additional Information**: - **Margin of Error (E)**: The margin of error is the range within which the true proportion is expected to fall. In this task, the margin of error is 0.04. - **Proportion (p)**: The estimated proportion from the survey is 0.38. - **Confidence Level**: The confidence level for this interval is 95%. **Graphical/Diagrammatic Explanation**: No graphs or diagrams are present in the provided text. Should there be any, they would be explained in detail to assist in understanding the data and the necessary calculations. For further questions and explanations, references to statistical formulas and methods to calculate sample size can be provided. ---
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