Answered: The Chancellor wants you to calculate…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 11MCQ

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Question

The Chancellor wants you to calculate the sample size needed with a margin of error of 15, 99% confidence, and a population standard deviation of 22.

Expert Solution

Step 1

$\mathbf{Solution}$

$\mathrm{\mathbf{given}:}$

$\mathrm{Margin \;of\; error \;(E)=15}$

$\mathrm{Population\;standard\; deviation\;(\sigma)=12}$

Since we know population standard deviation, use z-distribution to find z-critical value.

Find z-critical value:

For the two-tail test, Area on each tail.

Area to the left of the normal curve = 1-0.005 = 0.995

Refer Standard normal table/Z-table, Lookup for z-score corresponding to area 0.995 to the left of the normal curve
OR
Use excel formula "=NORM.S.INV(0.995)" to find the z-score.

$\mathrm{P(Z<\mathbf{2.576})=0.995}$

$\mathrm{\therefore z_{\frac{\alpha }{2}}=2.576}$

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