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
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
**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.
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.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman