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Assume that a random sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. nbsp 90 % confidence; the sample size is 3200 comma of which 15 % are successes 90% confidence; the sample size is 3200, of which 15% are successes The margin of error Eequals=nothing. ​(Round to four decimal places as​ needed.)

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JeanaShupp

Answer: The margin of error E = 0.0104

Step-by-step explanation:

The formula to find the margin of error that corresponds to the given statistics and confidence level for population proportion is given by :-

[tex]E=z*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex] , where

n= Sample size

[tex]\hat{p}[/tex] = Sample proportion

z* = critical value.

As per given , we have

n= 3200

[tex]\hat{p}=0.15[/tex]

Confidence level : 90%

The critical z-value for 90% confidence is z* = =1.645[By z-table]

Substitute all values in the formula , we get

[tex]E=(1.645)\sqrt{\dfrac{0.15(1-0.15)}{3200}}[/tex]

[tex]E=(1.645)\sqrt{0.00003984375}[/tex]

[tex]E=(1.645)(0.00631219058648)=0.0103835535148\approx0.0104[/tex]

Hence, the margin of error E = 0.0104

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