A past survey of 1,068,000 students taking a standardized test revealed that 8.2% of the students were planning on studying engineering in college. In a recent survey of 1,476,000 students taking the SAT, 9.2% of the students were planning to study engineering. Construct a 90% confidence interval for the difference between proportions \( p_1 - p_2 \) by using the following inequality: Assume the samples are random and independent. \[ \left( \hat{p}_1 - \hat{p}_2 \right) - z_c \sqrt{ \frac{ \hat{p}_1 \hat{q}_1 }{ n_1 } + \frac{ \hat{p}_2 \hat{q}_2 }{ n_2 } } < p_1 - p_2 < \left( \hat{p}_1 - \hat{p}_2 \right) + z_c \sqrt{ \frac{ \hat{p}_1 \hat{q}_1 }{ n_1 } + \frac{ \hat{p}_2 \hat{q}_2 }{ n_2 } } \] The confidence interval is \([ \_\_\_\_ < p_1 - p_2 < \_\_\_\_ ]\) (Round to three decimal places as needed.)
A past survey of 1,068,000 students taking a standardized test revealed that 8.2% of the students were planning on studying engineering in college. In a recent survey of 1,476,000 students taking the SAT, 9.2% of the students were planning to study engineering. Construct a 90% confidence interval for the difference between proportions \( p_1 - p_2 \) by using the following inequality: Assume the samples are random and independent. \[ \left( \hat{p}_1 - \hat{p}_2 \right) - z_c \sqrt{ \frac{ \hat{p}_1 \hat{q}_1 }{ n_1 } + \frac{ \hat{p}_2 \hat{q}_2 }{ n_2 } } < p_1 - p_2 < \left( \hat{p}_1 - \hat{p}_2 \right) + z_c \sqrt{ \frac{ \hat{p}_1 \hat{q}_1 }{ n_1 } + \frac{ \hat{p}_2 \hat{q}_2 }{ n_2 } } \] The confidence interval is \([ \_\_\_\_ < p_1 - p_2 < \_\_\_\_ ]\) (Round 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
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![A past survey of 1,068,000 students taking a standardized test revealed that 8.2% of the students were planning on studying engineering in college. In a recent survey of 1,476,000 students taking the SAT, 9.2% of the students were planning to study engineering. Construct a 90% confidence interval for the difference between proportions \( p_1 - p_2 \) by using the following inequality:
Assume the samples are random and independent.
\[
\left( \hat{p}_1 - \hat{p}_2 \right) - z_c \sqrt{ \frac{ \hat{p}_1 \hat{q}_1 }{ n_1 } + \frac{ \hat{p}_2 \hat{q}_2 }{ n_2 } } < p_1 - p_2 < \left( \hat{p}_1 - \hat{p}_2 \right) + z_c \sqrt{ \frac{ \hat{p}_1 \hat{q}_1 }{ n_1 } + \frac{ \hat{p}_2 \hat{q}_2 }{ n_2 } }
\]
The confidence interval is \([ \_\_\_\_ < p_1 - p_2 < \_\_\_\_ ]\)
(Round to three decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69841bf7-b9f0-4fc9-8153-6ebe52f9298f%2Fde29132e-478c-44b4-8d4e-ec3c2a961915%2Fc86hwee.jpeg&w=3840&q=75)
Transcribed Image Text:A past survey of 1,068,000 students taking a standardized test revealed that 8.2% of the students were planning on studying engineering in college. In a recent survey of 1,476,000 students taking the SAT, 9.2% of the students were planning to study engineering. Construct a 90% confidence interval for the difference between proportions \( p_1 - p_2 \) by using the following inequality:
Assume the samples are random and independent.
\[
\left( \hat{p}_1 - \hat{p}_2 \right) - z_c \sqrt{ \frac{ \hat{p}_1 \hat{q}_1 }{ n_1 } + \frac{ \hat{p}_2 \hat{q}_2 }{ n_2 } } < p_1 - p_2 < \left( \hat{p}_1 - \hat{p}_2 \right) + z_c \sqrt{ \frac{ \hat{p}_1 \hat{q}_1 }{ n_1 } + \frac{ \hat{p}_2 \hat{q}_2 }{ n_2 } }
\]
The confidence interval is \([ \_\_\_\_ < p_1 - p_2 < \_\_\_\_ ]\)
(Round to three decimal places as needed.)
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