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According to the 2017 American Community Survey of about 73950 American women ages 25 to 34, the survey reported a 95% confidence interval of 39.45% to 40.15% of American women in that group have bachelor's degrees or higher. (a) Interpret this interval in context of the data. The researchers can be 95% confident that the sample proportion of American women ages 25 to 34 with bachelor's degrees is between 39.45% and 40.15% The researchers can be 95% confident that the true population proportion of American women ages 25 to 34 have bachelor's degrees is between 39.45% and 40.15% 95% of surveys will report a proportion of American women ages 25 to 34 with bachelor's degrees is between 39.45% and 40.15% (b) Suppose the researchers think a 99% confidence level would be more appropriate for this interval. Will this new interval be smaller or larger than the 95% confidence interval? smaller larger (c) If a new survey were to be done with 500 American women in this age group, would the standard error of the estimate be larger, smaller, or about the same? smaller about the same larger

According to the 2017 American Community Survey of about 73950 American women ages 25 to 34, the survey reported a 95% confidence interval of 39.45% to 40.15% of American women in that group have bachelor's degrees or higher. (a) Interpret this interval in context of the data. The researchers can be 95% confident that the sample proportion of American women ages 25 to 34 with bachelor's degrees is between 39.45% and 40.15% The researchers can be 95% confident that the true population proportion of American women ages 25 to 34 have bachelor's degrees is between 39.45% and 40.15% 95% of surveys will report a proportion of American women ages 25 to 34 with bachelor's degrees is between 39.45% and 40.15% (b) Suppose the researchers think a 99% confidence level would be more appropriate for this interval. Will this new interval be smaller or larger than the 95% confidence interval? smaller larger (c) If a new survey were to be done with 500 American women in this age group, would the standard error of the estimate be larger, smaller, or about the same? smaller about the same larger

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Confidence Intervals and Their Interpretation In a survey conducted as part of the 2017 American Community Survey, data was collected from approximately 73,950 American women ages 25 to 34. The survey reported a 95% confidence interval of 39.45% to 40.15% for the proportion of American women in this age group who have bachelor’s degrees or higher. #### (a) Interpretation of the Confidence Interval The confidence interval provides a range within which the true population proportion is expected to fall. This can be interpreted in the context of the survey data as follows: - **Option 1:** The researchers can be 95% confident that the sample proportion of American women ages 25 to 34 with bachelor’s degrees is between 39.45% and 40.15%. - **Option 2 (Correct Answer):** The researchers can be 95% confident that the true population proportion of American women ages 25 to 34 who have bachelor’s degrees is between 39.45% and 40.15%. - **Option 3:** 95% of surveys will report a proportion of American women ages 25 to 34 with bachelor’s degrees between 39.45% and 40.15%. #### (b) Effect of Increasing Confidence Level Suppose the researchers aim to use a 99% confidence level instead of a 95% confidence level. The impact on the confidence interval would be: - **Smaller** - **Larger (Correct Answer)** Increasing the confidence level to 99% would result in a wider confidence interval because a higher confidence level means that we need to be more certain that the interval contains the true population parameter, which requires accounting for more variability. #### (c) Impact of Sample Size on Standard Error If a new survey is conducted with 500 American women in the 25 to 34 age group, the standard error of the estimate would change as follows: - **Smaller** - **About the same** - **Larger (Correct Answer)** If the sample size is decreased from 73,950 to 500, the standard error of the estimate will increase because standard error is inversely proportional to the square root of the sample size. A smaller sample size results in a larger standard error, implying that there is more variability in the estimate.
Transcribed Image Text:### Confidence Intervals and Their Interpretation In a survey conducted as part of the 2017 American Community Survey, data was collected from approximately 73,950 American women ages 25 to 34. The survey reported a 95% confidence interval of 39.45% to 40.15% for the proportion of American women in this age group who have bachelor’s degrees or higher. #### (a) Interpretation of the Confidence Interval The confidence interval provides a range within which the true population proportion is expected to fall. This can be interpreted in the context of the survey data as follows: - **Option 1:** The researchers can be 95% confident that the sample proportion of American women ages 25 to 34 with bachelor’s degrees is between 39.45% and 40.15%. - **Option 2 (Correct Answer):** The researchers can be 95% confident that the true population proportion of American women ages 25 to 34 who have bachelor’s degrees is between 39.45% and 40.15%. - **Option 3:** 95% of surveys will report a proportion of American women ages 25 to 34 with bachelor’s degrees between 39.45% and 40.15%. #### (b) Effect of Increasing Confidence Level Suppose the researchers aim to use a 99% confidence level instead of a 95% confidence level. The impact on the confidence interval would be: - **Smaller** - **Larger (Correct Answer)** Increasing the confidence level to 99% would result in a wider confidence interval because a higher confidence level means that we need to be more certain that the interval contains the true population parameter, which requires accounting for more variability. #### (c) Impact of Sample Size on Standard Error If a new survey is conducted with 500 American women in the 25 to 34 age group, the standard error of the estimate would change as follows: - **Smaller** - **About the same** - **Larger (Correct Answer)** If the sample size is decreased from 73,950 to 500, the standard error of the estimate will increase because standard error is inversely proportional to the square root of the sample size. A smaller sample size results in a larger standard error, implying that there is more variability in the estimate.
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