Question

In a 2010 Pew Research study on trends in marriage and family, $4 \%$ of randomly selected respondents said that the trend of more single women having children is "a good thing." The $95 \%$ confidence interval is from $2.9 \%$ to $5.1 \%(n=1229)$. a) Interpret this interval in this context. b) Explain the meaning of "95\% confident" in this context.

Name: Problem 4, Chapter 18: Stats Data and Models
Uploaded: 2022-11-07T22:16:11-08:00
Duration: 2 min 10 s
Channel: James Kiss
Description: In a 2010 Pew Research study on trends in marriage and family, 4 % of randomly selected respondents said that the trend of more single women having children is "a good thing." The 95 % confidence interval is from 2.9 % to 5.1 %(n=1229). a) Interpret this interval in this context. b) Explain the meaning of "95% confident" in this context.

   In a 2010 Pew Research study on trends in marriage and family, $4 \%$ of randomly selected respondents said that the trend of more single women having children is "a good thing." The $95 \%$ confidence interval is from $2.9 \%$ to $5.1 \%(n=1229)$.
a) Interpret this interval in this context.
b) Explain the meaning of "95\% confident" in this context.

Stats Data and Models

Richard D. De Veaux,… 4th Edition

Chapter 18, Problem 4

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Solved by Expert James Kiss

11/07/2022

Step 1

The confidence interval is a range of values, derived from the statistical analysis of the sample data, which is likely to contain the value of an unknown population parameter. In this case, the confidence interval is from $2.9\%$ to $5.1\%$. This means that we Show more…

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In a 2010 Pew Research study on trends in marriage and family, $4 \%$ of randomly selected respondents said that the trend of more single women having children is "a good thing." The $95 \%$ confidence interval is from $2.9 \%$ to $5.1 \%(n=1229)$. a) Interpret this interval in this context. b) Explain the meaning of "95\% confident" in this context.

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Key Concepts

Confidence Level

The confidence level, expressed as a percentage such as 95%, represents the long-run proportion of confidence intervals that would contain the true parameter if the same sampling process were repeated many times. This level reflects the reliability of the estimation method rather than the probability that any one specific interval includes the parameter.

Confidence Interval

A confidence interval is a calculated range derived from sample data that estimates the possible values of an unknown population parameter. In statistical inference, it conveys the degree of uncertainty associated with a sample estimate, suggesting that the true parameter likely lies within this range if the study were repeated under similar conditions.

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