### Constructing a Confidence Interval for a Population ProportionIn this lesson, we will use sample data and a given confidence level to illustrate how to complete certain statistical calculations. This example involves a drug used to prevent blood clots in patients, where clinical trials were conducted, and results were recorded. Let's go through the steps to estimate the population proportion and construct a confidence interval.#### Scenario:A drug is used to help prevent blood clots in certain patients. In clinical trials, among 4364 patients treated with the drug, 129 developed the adverse reaction of nausea. We will construct a 95% confidence interval for the proportion of adverse reactions.#### Steps to Follow:1. **Find the best point estimate of the population proportion \( p \).**2. **Identify the margin of error \( E \).**3. **Construct the confidence interval.**4. **Interpret the confidence interval correctly.**### Calculations:#### a) Find the best point estimate of the population proportion \( p \).The best point estimate for the population proportion \( p \) is given by the sample proportion \( \hat{p} \). The formula is:\[ \hat{p} = \frac{x}{n} \]where \( x \) is the number of patients who developed nausea, and \( n \) is the total number of patients in the trial.#### b) Identify the value of the margin of error \( E \).The margin of error \( E \) can be calculated using the formula:\[ E = Z_{\alpha/2} \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \]where \( Z_{\alpha/2} \) is the critical value from the z-distribution for a 95% confidence interval.#### c) Construct the confidence interval.The confidence interval can be constructed using the formula:\[ \hat{p} - E < p < \hat{p} + E \]#### d) Statement selection:Make a correct interpretation of the obtained confidence interval.### Explanation of a Graph or Diagram (if any):In the example, there are no graphs or diagrams shown, but if there were any, they would typically illustrate the normal distribution curve, the critical value, and the area representing the confidence interval.### Conclusion:After performing these calculations, you will be able to construct a confidence interval for the population proportion and interpret it correctly. Statistically,

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Use the sample data and confidence level given below to complete parts (a) through (d). A drug is used to help prevent blood clots in certain patients. In clinical trials, among 4364 patients treated with the drug, 129 developed the adverse reaction of nausea, Construct a 95% c proportion of adverse reactions. a) Find the best point estimate of the population proportion p. (Round to three decimal places as needed.) b) Identify the value of the margin of error E. (Round to three 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. 95% of sample proportions will fall between the lower bound and the upper bound. O B. One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion. OC. One has 95% confidence that the sample proportion equal to the population proportion. O D. There is a 95% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

Use the sample data and confidence level given below to complete parts (a) through (d). A drug is used to help prevent blood clots in certain patients. In clinical trials, among 4364 patients treated with the drug, 129 developed the adverse reaction of nausea, Construct a 95% c proportion of adverse reactions. a) Find the best point estimate of the population proportion p. (Round to three decimal places as needed.) b) Identify the value of the margin of error E. (Round to three 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. 95% of sample proportions will fall between the lower bound and the upper bound. O B. One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion. OC. One has 95% confidence that the sample proportion equal to the population proportion. O D. There is a 95% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

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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