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Since the criteria for constructing a confidence interval for the population proportion p have been met, the confidence interval will have the following form where p is the sample proportion, the z critical value captures the central area equal to the confidence level as a proportion, and n is the sample size. p(1 - p) p + (z critical value) We have already determined p = 0.25 and n = 1,860, so must now determine the z critical value that will be used. For a 95% confidence interval, we will be capturing the central area of 0.95 under the z curve between -z* and z*. To find z*, recall the entire area under the z curve is 1. The remaining area of 1 - 0.95 = 0.05 will be split evenly between the lower and upper tails of the curve. That is, both the lower and upper tails of the curve will each have an area of (0.05): This will be added to the central area of 0.95, so the total area to the left of the desired z is SALT to find the value of z, rounding the result to two decimal places.

Since the criteria for constructing a confidence interval for the population proportion p have been met, the confidence interval will have the following form where p is the sample proportion, the z critical value captures the central area equal to the confidence level as a proportion, and n is the sample size. p(1 - p) p + (z critical value) We have already determined p = 0.25 and n = 1,860, so must now determine the z critical value that will be used. For a 95% confidence interval, we will be capturing the central area of 0.95 under the z curve between -z* and z*. To find z*, recall the entire area under the z curve is 1. The remaining area of 1 - 0.95 = 0.05 will be split evenly between the lower and upper tails of the curve. That is, both the lower and upper tails of the curve will each have an area of (0.05): This will be added to the central area of 0.95, so the total area to the left of the desired z is SALT to find the value of z, rounding the result to two decimal places.

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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Since the criteria for constructing a confidence interval for the population proportion p have been met, the confidence interval will have the following form where p is the sample proportion, the z critical value captures the central area equal to the confidence level as a proportion, and n is the sample size. p(1 - p) p + (z critical value) We have already determined p = 0.25 and n = 1,860, so must now determine the z critical value that will be used. For a 95% confidence interval, we will be capturing the central area of 0.95 under the z curve between -z* and z*. To find z*, recall the entire area under the z curve is 1. The remaining area of 1 - 0.95 = 0.05 will be split evenly between the lower and upper tails of the curve. That is, both the lower and upper tails of the curve will each have an area of (0.05): This will be added to the central area of 0.95, so the total area to the left of the desired z is Use SALT to find the value of z, rounding the result to two decimal places.
Transcribed Image Text:Since the criteria for constructing a confidence interval for the population proportion p have been met, the confidence interval will have the following form where p is the sample proportion, the z critical value captures the central area equal to the confidence level as a proportion, and n is the sample size. p(1 - p) p + (z critical value) We have already determined p = 0.25 and n = 1,860, so must now determine the z critical value that will be used. For a 95% confidence interval, we will be capturing the central area of 0.95 under the z curve between -z* and z*. To find z*, recall the entire area under the z curve is 1. The remaining area of 1 - 0.95 = 0.05 will be split evenly between the lower and upper tails of the curve. That is, both the lower and upper tails of the curve will each have an area of (0.05): This will be added to the central area of 0.95, so the total area to the left of the desired z is Use SALT to find the value of z, rounding the result to two decimal places.
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