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It is thought that not as many Americans buy presents to celebrate Valentine's Day anymore. A random sample of 4000 Americans yielded 2200 who bought their significant other a present and celebrated Valentine's Day. Estimate the true proportion of all Americans who celebrate Valentine's Day using a 90% confidence interval. Express the answer in the form p ± E and round to the nearest ten- thousandth.

It is thought that not as many Americans buy presents to celebrate Valentine's Day anymore. A random sample of 4000 Americans yielded 2200 who bought their significant other a present and celebrated Valentine's Day. Estimate the true proportion of all Americans who celebrate Valentine's Day using a 90% confidence interval. Express the answer in the form p ± E and round to the nearest ten- thousandth.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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**Provide an appropriate response.** It is thought that not as many Americans buy presents to celebrate Valentine’s Day anymore. A random sample of 4000 Americans yielded 2200 who bought their significant other a present and celebrated Valentine’s Day. Estimate the true proportion of all Americans who celebrate Valentine’s Day using a 90% confidence interval. Express the answer in the form \( \hat{p} \pm E \) and round to the nearest ten-thousandth. --- - \(0.4375 \pm 0.0129\) - \(0.5625 \pm 0.0129\) - \(0.4375 \pm 0.4048\) - \(0.5625 \pm 0.4048\) --- **Explanation of Possible Answers:** 1. **0.4375 ± 0.0129**: This option represents a proportion of 0.4375 with an error margin of 0.0129. 2. **0.5625 ± 0.0129**: This option represents a proportion of 0.5625 with an error margin of 0.0129. 3. **0.4375 ± 0.4048**: This option represents a proportion of 0.4375 with an error margin of 0.4048. 4. **0.5625 ± 0.4048**: This option represents a proportion of 0.5625 with an error margin of 0.4048. **Detail Analysis:** The correct calculation involves estimating the proportion (p̂) of the sample and determining the error margin (E) at a 90% confidence level. Given the sample size and responses, the statistical methods should lead you to one of the presented answers. By evaluating these options, you can verify the most accurate estimate for the true proportion of Americans who celebrate Valentine’s Day.
Transcribed Image Text:**Provide an appropriate response.** It is thought that not as many Americans buy presents to celebrate Valentine’s Day anymore. A random sample of 4000 Americans yielded 2200 who bought their significant other a present and celebrated Valentine’s Day. Estimate the true proportion of all Americans who celebrate Valentine’s Day using a 90% confidence interval. Express the answer in the form \( \hat{p} \pm E \) and round to the nearest ten-thousandth. --- - \(0.4375 \pm 0.0129\) - \(0.5625 \pm 0.0129\) - \(0.4375 \pm 0.4048\) - \(0.5625 \pm 0.4048\) --- **Explanation of Possible Answers:** 1. **0.4375 ± 0.0129**: This option represents a proportion of 0.4375 with an error margin of 0.0129. 2. **0.5625 ± 0.0129**: This option represents a proportion of 0.5625 with an error margin of 0.0129. 3. **0.4375 ± 0.4048**: This option represents a proportion of 0.4375 with an error margin of 0.4048. 4. **0.5625 ± 0.4048**: This option represents a proportion of 0.5625 with an error margin of 0.4048. **Detail Analysis:** The correct calculation involves estimating the proportion (p̂) of the sample and determining the error margin (E) at a 90% confidence level. Given the sample size and responses, the statistical methods should lead you to one of the presented answers. By evaluating these options, you can verify the most accurate estimate for the true proportion of Americans who celebrate Valentine’s Day.
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