Question

What sample size is needed to give a margin of error within
±2.5% in estimating a population proportion with 99% confidence? An
initial small sample has p^=0.78.

Round the answer up to the nearest integer.

Answer #1

Solution:

Given that:

E= 0.025

= 0.78

1 - = 1 - 0.78= 0.22

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_{/2}
= Z_{0.005} = 2.576

sample size = (Z_{/2}
/ E)^{2} * * (1 - )
_{ }

_{ } = (2.576 / 0.025)^{2} * (0.78 *
0.22)

= 1821.92

**sample size = 1822**

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Round your answer up to the nearest integer.
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Round to nearest whole integer.

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Use z-values rounded to three decimal places. Round your answer
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Find the sample size needed to give, with 95% confidence, a
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n =

Chapter 6, Section 2-CI, Exercise 110
What Influences the Sample Size Needed?
In this exercise, we examine the effect of the margin of error on
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Assume that we use ά =30 as out estimate of the standard deviation
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Round your answers up to the nearest integer.
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