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Chapter 8: Q. 51 (page 498)

51. You want to design a study to estimate the proportion of students at your school who agree with the statement, “The student government is an effective organization for expressing the needs of students to the administration.” You will use a 95% confidence interval, and you would like the margin of error to be 0.05 or less. The minimum sample size required is
(a) 22. (b) 271. (c) 385. (d) 769. (e) 1795.

Short Answer

Expert verified

The correct answer is option (c) 385.

Step by step solution

01

Given information

To find the minimum sample size required for 95%confidence interval, and the margin of error to be 0.05 or less.

02

Explanation

Let, mirror of error is E=0.05.

Determine the sample size as:

p^unknown: n=zα/220.25E2

Using table A, for confidence level 95%,
zα/2=1.96
p^ is unknown, then the sample size is:
n=zα/220.25E2

=1.962×0.250.052

≈385

As a result, option (c) 385 is correct.

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Interpret the confidence level.

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