We wish to estimate what percent of adult residents in a certain county are parents. Out of 200 adult residents sampled, 166 had kids. Based on this, construct a 99% confidence interval for the proportion T of adult residents who are parents in this county. Give your answers as decimals, to three places.
We wish to estimate what percent of adult residents in a certain county are parents. Out of 200 adult residents sampled, 166 had kids. Based on this, construct a 99% confidence interval for the proportion T of adult residents who are parents in this county. Give your answers as decimals, to three places.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![**Estimating the Proportion of Adult Residents who are Parents**
In this problem, we aim to estimate what percentage of adult residents in a specific county are parents. A sample of 200 adult residents was surveyed, and 166 of them had children. Using this information, we will construct a 99% confidence interval for the proportion (π) of adult residents who are parents in this county.
To calculate the confidence interval, input your answers as decimals to three decimal places in the boxes provided:
\[ \_ \ \ \ < \ \ \pi \ \ < \ \_\]
**Instructions:**
1. Verify the sample size (n = 200) and the number of parents in the sample (x = 166).
2. Use the sampling proportion (\(\hat{p} = \frac{x}{n}\)) as the point estimate.
3. Determine the standard error for the proportion.
4. Find the critical value for a 99% confidence level.
5. Calculate the margin of error using the critical value and the standard error.
6. Construct the confidence interval by adding and subtracting the margin of error from the point estimate.
This process helps to estimate the proportion of adult residents who are parents within a specified level of confidence, providing valuable insights for demographic and social research within the county.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa218d9b0-33cd-49fb-8966-615774819802%2F6c55ebdc-4390-43fe-bf76-9ed21d3098f8%2Fpc4sono_processed.png&w=3840&q=75)
Transcribed Image Text:**Estimating the Proportion of Adult Residents who are Parents**
In this problem, we aim to estimate what percentage of adult residents in a specific county are parents. A sample of 200 adult residents was surveyed, and 166 of them had children. Using this information, we will construct a 99% confidence interval for the proportion (π) of adult residents who are parents in this county.
To calculate the confidence interval, input your answers as decimals to three decimal places in the boxes provided:
\[ \_ \ \ \ < \ \ \pi \ \ < \ \_\]
**Instructions:**
1. Verify the sample size (n = 200) and the number of parents in the sample (x = 166).
2. Use the sampling proportion (\(\hat{p} = \frac{x}{n}\)) as the point estimate.
3. Determine the standard error for the proportion.
4. Find the critical value for a 99% confidence level.
5. Calculate the margin of error using the critical value and the standard error.
6. Construct the confidence interval by adding and subtracting the margin of error from the point estimate.
This process helps to estimate the proportion of adult residents who are parents within a specified level of confidence, providing valuable insights for demographic and social research within the county.
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