### Constructing a Confidence Interval for the Difference in Population ProportionsIn this lesson, we will learn how to construct a confidence interval for the difference between two population proportions, \( p_1 - p_2 \), using the given data and a specified confidence level. This is useful when you want to compare two groups and understand the range in which the true difference in their proportions lies with a certain level of confidence.#### Given Data:- \( x_1 = 387 \)- \( n_1 = 536 \)- \( x_2 = 415 \)- \( n_2 = 551 \)- Confidence level: 90%#### Step-by-Step Process:1. **Identify the given values**: - \( x_1 \) and \( n_1 \) are the sample successes and sample size for the first population. - \( x_2 \) and \( n_2 \) are the sample successes and sample size for the second population.2. **Calculate the sample proportions**: - Sample proportion for the first population: \( \hat{p}_1 = \frac{x_1}{n_1} \) - Sample proportion for the second population: \( \hat{p}_2 = \frac{x_2}{n_2} \)3. **Determine the difference between the sample proportions**: - Difference: \( \hat{p}_1 - \hat{p}_2 \)4. **Calculate the standard error of the difference between the two proportions**: - Standard Error (SE): \( \sqrt{\frac{\hat{p}_1 (1 - \hat{p}_1)}{n_1} + \frac{\hat{p}_2 (1 - \hat{p}_2)}{n_2}} \)5. **Find the Z-score corresponding to the 90% confidence level**: - Z-score for 90% confidence is typically 1.645 (this can be found from Z-tables or statistical tools)6. **Calculate the margin of error**: - Margin of Error (ME): \( Z \times SE \)7. **Construct the confidence interval**: - Lower bound: \( (\hat{p}_1 - \hat{p}_2) - ME \) - Upper bound: \( (\hat{p}_1 - \hat{p

Name: ### Constructing a Confidence Interval for the Difference in Populati
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: ### Constructing a Confidence Interval for the Difference in Population ProportionsIn this lesson, we will learn how to construct a confidence interval for the difference between two population proportions, \( p_1 - p_2 \), using the given data and

Answered: Image /qna-images/answer/1a35451a-c417-4650-ab00-24d21f200759.jpg

Math

Statistics

Construct a confidence interval for p, -P2 at the given level of confidence. X1 = 387, n, = 536, x2 = 415, n2 = 551, 90% confidence The researchers are % confident the difference between the two population proportions, p, -P2, is between and (Use ascending order. Type an integer or decimal rounded to three decimal places as needed.)

Construct a confidence interval for p, -P2 at the given level of confidence. X1 = 387, n, = 536, x2 = 415, n2 = 551, 90% confidence The researchers are % confident the difference between the two population proportions, p, -P2, is between and (Use ascending order. Type an integer or decimal rounded to three decimal places as needed.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Find the value:
Use the confidence interval to find the margin of error and the sample mean. (0.636, 0.760)
Use the confidence interval to find the margin of error and the sample mean. (0.196,0.300) The margin of error is
Help
the population You measure 27 dogs' weights, and find they have a mean weight of 58 ounces. standard deviation is 7 ounces. Based on this, construct a 95% confidence interval for the true population mean dog weight. Give your answers as decimals, to two places - ounces Enter an integer or decimal number [more..]
Use the Student's t distribution to find tc for a 0.90 confidence level when the sample is 25. (Round your answer to three decimal places.)
Use the confidence interval to find the margin of error and the sample mean. (0.174,0.290) The margin of error is Sample mean is
Researchers studied the mean egg length (in millimeters) for a bird population. After taking a random sample of eggs, they obtained a 95% confidence interval of (45,60). What is the value of the margin of error? Choose the correct answer below. A. 15 mm B. 52.5 mm O c. 7.5 mm O D. 1.96
Find the margin of error at a 80% confidence level for estimating the population mean if n = 16, = 32 and s = 10. Round your answer to 2 decimal places.
Use the Student's t distribution to find tc for a 0.95 confidence level when the sample is 29. (Round your answer to three decimal places.)
Use the confidence interval to find the margin of error and the sample mean. (0.576,0.760) The margin of error is The sample mean is
Set up the null and alternate hypotheses to test whether the population mean is equal to 10 when you have a sample mean. H0: Ha: