A NEW STUDY OF PUBLIC OPINION IS DESIGNED. THE GOAL IS TO ESTIMATE THE PROPORTIO

Question

A NEW STUDY OF PUBLIC OPINION IS DESIGNED. THE GOAL IS TO ESTIMATE THE PROPORTION OF DRIVERS WILLING TO TRADE IN THEIR CARS. ANSWER QUESTIONS RELATED TO THE SMALLEST SAMPLE SIZE NEEDED FOR THE STUDY TO SATISFY THE MARGIN OF ERROR.

(A) AT THE 90% CONFIDENCE LEVEL, WHAT IS THE SMALLEST SAMPLE SIZE NEEDED IF THE MARGIN OF ERROR FOR THE POPULATION PROPORTION SHOULD BE BELOW 3.25%?

CRITICAL VALUE

THE SMALLEST SAMPLE SIZE

(B) AT THE 95% CONFIDENCE LEVEL, WHAT IS THE SMALLEST SAMPLE SIZE NEEDED IF THE MARGIN OF ERROR FOR THE POPULATION PROPORTION SHOULD BE AT MOST 4.5%?

CRITICAL VALUE

THE SMALLEST SAMPLE SIZE

(C) AT THE 99% CONFIDENCE LEVEL, WHAT IS THE SMALLEST SAMPLE SIZE NEEDED IF THE MARGIN OF ERROR FOR THE POPULATION PROPORTION SHOULD BE WITHIN 3%?

CRITICAL VALUE

THE SMALLEST SAMPLE SIZE

Explanation / Answer

a.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.1 is = 1.64
Samle Proportion = 0.0325
ME = 0.5
n = ( 1.64 / 0.5 )^2 * 0.0325*0.9675
= 0.338284 ~ 1
b.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.05 is = 1.96
Samle Proportion = 0.045
ME = 0.5
n = ( 1.96 / 0.5 )^2 * 0.045*0.955
= 0.660371 ~ 1
c.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.01 is = 2.58
Samle Proportion = 0.03
ME = 0.5
n = ( 2.58 / 0.5 )^2 * 0.03*0.97
= 0.774805 ~ 1

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