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Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they acted to annoy a bad driver. In the poll, n= 2673, and x= 1061 who said that they honked. Use a 99% confidence level. n3D Click the icon to view a table of z scores. (Round to three decimal places as needed.) b) Identify the value of the margin of error E. D E = (Round to four decimal places as needed.) c) Construct the confidence interval. (Round to three decimal places as needed.) d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below. O A. There is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound. O B. 99% of sample proportions will fall between the lower bound and the upper bound. OC. One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion. O D. One has 99% confidence that the sample proportion is equal to the population proportion.

Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they acted to annoy a bad driver. In the poll, n= 2673, and x= 1061 who said that they honked. Use a 99% confidence level. n3D Click the icon to view a table of z scores. (Round to three decimal places as needed.) b) Identify the value of the margin of error E. D E = (Round to four decimal places as needed.) c) Construct the confidence interval. (Round to three decimal places as needed.) d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below. O A. There is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound. O B. 99% of sample proportions will fall between the lower bound and the upper bound. OC. One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion. O D. One has 99% confidence that the sample proportion is equal to the population proportion.

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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**Positive Z Scores Table** This table displays the standard normal (z) distribution and the cumulative area from the left for positive z-scores. It helps determine the probability that a statistic is less than a given z-score, assuming a normal distribution. ### Table Explanation The table is divided into three sections: 1. **Left Column (z)**: This column represents the whole number and first decimal place of the z-score. For example, for a z-score of 1.2, this column would show "1.2". 2. **Top Row (.00 to .09)**: These columns represent the second decimal place of the z-score. To find the probability for a z-score of 1.23, for instance, locate "1.2" in the left column and ".03" at the top. 3. **Values in the Table**: The values inside the table indicate the cumulative probability from the left up to that z-score. For a z-score of 1.23, follow the row "1.2" across to the column ".03" to find the cumulative probability of 0.8907, meaning there is an 89.07% probability that a value is below this z-score. ### Graph A bell curve diagram above the table represents the standard normal distribution with shaded areas indicating the left cumulative area corresponding to z-scores. This table is essential for statistical analysis, providing a quick reference to understand standard deviations and their impact on data within the context of a normal distribution.
Transcribed Image Text:**Positive Z Scores Table** This table displays the standard normal (z) distribution and the cumulative area from the left for positive z-scores. It helps determine the probability that a statistic is less than a given z-score, assuming a normal distribution. ### Table Explanation The table is divided into three sections: 1. **Left Column (z)**: This column represents the whole number and first decimal place of the z-score. For example, for a z-score of 1.2, this column would show "1.2". 2. **Top Row (.00 to .09)**: These columns represent the second decimal place of the z-score. To find the probability for a z-score of 1.23, for instance, locate "1.2" in the left column and ".03" at the top. 3. **Values in the Table**: The values inside the table indicate the cumulative probability from the left up to that z-score. For a z-score of 1.23, follow the row "1.2" across to the column ".03" to find the cumulative probability of 0.8907, meaning there is an 89.07% probability that a value is below this z-score. ### Graph A bell curve diagram above the table represents the standard normal distribution with shaded areas indicating the left cumulative area corresponding to z-scores. This table is essential for statistical analysis, providing a quick reference to understand standard deviations and their impact on data within the context of a normal distribution.
**Transcription and Explanation for an Educational Website** --- **Title: Understanding Confidence Intervals in Poll Data** **Introduction:** When conducting surveys or polls, it's crucial to analyze the data to make inferences about a larger population. Confidence intervals help us determine the range within which the true population parameter likely falls. In this exercise, we use data from a poll to construct a 99% confidence interval for a population proportion. **Poll Scenario:** A research institute conducted a poll asking respondents if they acted to annoy a bad driver. In this survey: - Total respondents (n): 2,673 - Respondents who said they honked (x): 1,061 - Confidence level: 99% **Steps to Calculate:** 1. **Find the Sample Proportion (p̂):** - Formula: \( p̂ = \frac{x}{n} \) - Round to three decimal places. 2. **Identify the Margin of Error (E):** - Formula: \( E = Z \times \sqrt{\frac{p̂(1-p̂)}{n}} \) - Use the Z-score for a 99% confidence level. - Round to four decimal places. 3. **Construct the Confidence Interval:** - Formula: \( p̂ - E < p < p̂ + E \) - Round each component to three decimal places. 4. **Interpret the Confidence Interval:** - Choose the correct interpretation from the following options: **Options:** - **A:** There is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound. - **B:** 99% of sample proportions will fall between the lower bound and the upper bound. - **C:** One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion. - **D:** One has 99% confidence that the sample proportion is equal to the population proportion. **Conclusion:** Understanding and correctly interpreting confidence intervals is crucial for making statistical inferences. This exercise highlights the methodology for calculating them and emphasizes the importance of confidence in the estimations it provides.
Transcribed Image Text:**Transcription and Explanation for an Educational Website** --- **Title: Understanding Confidence Intervals in Poll Data** **Introduction:** When conducting surveys or polls, it's crucial to analyze the data to make inferences about a larger population. Confidence intervals help us determine the range within which the true population parameter likely falls. In this exercise, we use data from a poll to construct a 99% confidence interval for a population proportion. **Poll Scenario:** A research institute conducted a poll asking respondents if they acted to annoy a bad driver. In this survey: - Total respondents (n): 2,673 - Respondents who said they honked (x): 1,061 - Confidence level: 99% **Steps to Calculate:** 1. **Find the Sample Proportion (p̂):** - Formula: \( p̂ = \frac{x}{n} \) - Round to three decimal places. 2. **Identify the Margin of Error (E):** - Formula: \( E = Z \times \sqrt{\frac{p̂(1-p̂)}{n}} \) - Use the Z-score for a 99% confidence level. - Round to four decimal places. 3. **Construct the Confidence Interval:** - Formula: \( p̂ - E < p < p̂ + E \) - Round each component to three decimal places. 4. **Interpret the Confidence Interval:** - Choose the correct interpretation from the following options: **Options:** - **A:** There is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound. - **B:** 99% of sample proportions will fall between the lower bound and the upper bound. - **C:** One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion. - **D:** One has 99% confidence that the sample proportion is equal to the population proportion. **Conclusion:** Understanding and correctly interpreting confidence intervals is crucial for making statistical inferences. This exercise highlights the methodology for calculating them and emphasizes the importance of confidence in the estimations it provides.
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