Answered: The chancellor wants you to calculate…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 6E: List the sample space of each experiment. Tossing three coins

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The chancellor wants you to calculate the largest sample size needed with a margin error of 5% and 90% confidence.

Expert Solution

Step 1

When we don't have any prior information about the population proportion, we generally take it as 0.50. At a 90% confidence level, the z value is 1.645 which can be obtained by using the standard normal table. Now, the required sample size can be calculated as:

$n = \frac{z^{2} \times p (1 - p)}{E^{2}}$

Given:

z = 1.645 = The value at 90% confidence level

E = 0.05 = 5%

p = 0.50 ( As no prior information is given)

Substitute the given values in the above-mentioned formula as follows:

$n = \frac{z^{2} \times p (1 - p)}{E^{2}} = \frac{1 . 645^{2} \times 0.50 (1 - 0.50)}{0 . 05^{2}} = 270.60 ≃ 271$

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