Question 15 < > The 2010 General Social Survey asked 1235 US residents: "Do you think the use of marijuana should be made legal, or not?" 48% of the respondents said it should be made legal a) Is 48% a statistic or a parameter? O Statistic since it came from all U.S. residents Statistic since it came from a sample of U.S. residents O Parameter since it came from all U.S. residents O Parameter since it came from a sample of U.S. residents Submit All Parts b) Construct a 95% confidence interval for the proportion of US residents who think marijuana should be made legal and round your answer to 4 decimal places. Lower bound: Upper bound:
Question 15 < > The 2010 General Social Survey asked 1235 US residents: "Do you think the use of marijuana should be made legal, or not?" 48% of the respondents said it should be made legal a) Is 48% a statistic or a parameter? O Statistic since it came from all U.S. residents Statistic since it came from a sample of U.S. residents O Parameter since it came from all U.S. residents O Parameter since it came from a sample of U.S. residents Submit All Parts b) Construct a 95% confidence interval for the proportion of US residents who think marijuana should be made legal and round your answer to 4 decimal places. Lower bound: Upper bound:
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.2: Box-and-whisker Plots
Problem 1E
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![### Question 15
#### The 2010 General Social Survey asked 1235 U.S. residents: "Do you think the use of marijuana should be made legal, or not?" 48% of the respondents said it should be made legal.
**a) Is 48% a statistic or a parameter?**
- Statistic since it came from all U.S. residents
- Statistic since it came from a sample of U.S. residents
- Parameter since it came from all U.S. residents
- Parameter since it came from a sample of U.S. residents
**b) Construct a 95% confidence interval for the proportion of U.S. residents who think marijuana should be made legal and round your answer to 4 decimal places.**
- Lower bound: _______
- Upper bound: _______
[Submit All Parts]
---
### Explanation:
In part **(a)**, the question tests understanding of the distinction between a statistic and a parameter. A **statistic** is a characteristic or measure obtained by using the data values from a *sample*. A **parameter** is a characteristic or measure obtained by using all the data values from a *population*.
In part **(b)**, the task involves calculating a 95% confidence interval for the given proportion. This involves using the formula for the confidence interval for a proportion:
\[ \hat{p} \pm Z \cdot \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \]
where:
- \(\hat{p}\) is the sample proportion (0.48 in this case)
- \(Z\) is the Z-value corresponding to the 95% confidence level (1.96)
- \(n\) is the sample size (1235)
The specific steps include calculating the margin of error and then determining the lower and upper bounds of the confidence interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fef18d251-78af-4374-b6cb-89037e4b2414%2F8be8026e-4249-4dde-9d2f-97944b0dc0a6%2Fnu8djas_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 15
#### The 2010 General Social Survey asked 1235 U.S. residents: "Do you think the use of marijuana should be made legal, or not?" 48% of the respondents said it should be made legal.
**a) Is 48% a statistic or a parameter?**
- Statistic since it came from all U.S. residents
- Statistic since it came from a sample of U.S. residents
- Parameter since it came from all U.S. residents
- Parameter since it came from a sample of U.S. residents
**b) Construct a 95% confidence interval for the proportion of U.S. residents who think marijuana should be made legal and round your answer to 4 decimal places.**
- Lower bound: _______
- Upper bound: _______
[Submit All Parts]
---
### Explanation:
In part **(a)**, the question tests understanding of the distinction between a statistic and a parameter. A **statistic** is a characteristic or measure obtained by using the data values from a *sample*. A **parameter** is a characteristic or measure obtained by using all the data values from a *population*.
In part **(b)**, the task involves calculating a 95% confidence interval for the given proportion. This involves using the formula for the confidence interval for a proportion:
\[ \hat{p} \pm Z \cdot \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \]
where:
- \(\hat{p}\) is the sample proportion (0.48 in this case)
- \(Z\) is the Z-value corresponding to the 95% confidence level (1.96)
- \(n\) is the sample size (1235)
The specific steps include calculating the margin of error and then determining the lower and upper bounds of the confidence interval.
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