Question

Gandolf the Grey wants to find the height of an average Elf. Through magic, he is able to discover that the standard deviation for their height is 0.56 meters. He will allow for an error of 0.12 meters and wants to be 98% confident that he has found the true population mean. What is the minimum number of Elves must he measure for his study to be valid? [You would think if magic could find the standard deviation, it could find the mean. But I guess math is mightier than magic sometimes.]

Answer #1

Solution :

Given that,

standard deviation = =0.56

Margin of error = E = 0.12

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table )

sample size = n = [Z/2* / E] 2

n = ( 2.326* 0.56 / 0.12 )2

n =117.82

Sample size = n =118

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