Use the expression in the accompanying discussion of sample size to find the size of each sample if you want to estimate the difference between proportions of men and women who own smartphones. Assume that you want 95% confidence that your error is no more than 0.035. The sample should includemen and women.(Type whole numbers.) The sample size needed to estimate the difference between two populationproportions to within a margin of error E with a confidence level of 1 - a can befound by using the following expression:P191P292E=Zα/2 n₁ n₂Replace n₁ and n₂ by n in the preceding formula (assuming that both sampleshave the same size) and replace each of p₁, 9₁, P2, and q2 by 0.5 (because theirvalues are not known). Solving for n results in this expression:n=-α/22E²

Answered: Image /qna-images/answer/5bcec9c4-aee5-49ca-b61d-1247e333ce32.jpg

Answered: want 95% confidence that your error is…

want 95% confidence that your error is no more than 0.035. The sample should include men and women. (Type whole numbers.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 14PPS

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Question

Use the expression in the accompanying discussion of sample size to find the size of each sample if you want to estimate the difference between proportions of men and women who own smartphones. Assume that you want 95% confidence that your error is no more than 0.035.

The sample should include

men and women.

(Type whole numbers.)

The sample size needed to estimate the difference between two population
proportions to within a margin of error E with a confidence level of 1 - a can be
found by using the following expression:
P191
P292
E=Zα/2 n₁ n₂
Replace n₁ and n₂ by n in the preceding formula (assuming that both samples
have the same size) and replace each of p₁, 9₁, P2, and q2 by 0.5 (because their
values are not known). Solving for n results in this expression:
n=
-α/2
2E²

Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.

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