And I Q test is designed so that the main is 100 and the standard deviation is 1

Question

And I Q test is designed so that the main is 100 and the standard deviation is 15 for the population of normal adults find the sample size to estimate the mean IQ score a statistic students says that it can’t be said with 95 percent confidence that the meeting is with him for IQ points of the true me assume that Sigma equals 15 And I Q test is designed so that the main is 100 and the standard deviation is 15 for the population of normal adults find the sample size to estimate the mean IQ score a statistic students says that it can’t be said with 95 percent confidence that the meeting is with him for IQ points of the true me assume that Sigma equals 15

Explanation / Answer

we know that the margin of error is given as

MOE = z*SD/sqrt(n)

here we know that z = 1.96 for the 95% CI from the z table

and sd = 15

but MOE is not given here , the question is not phrased properly , suppose we want the MOE to be within 10%

so we put MOE as 0.1

0.01 = 1.96*15/sqrt(n)

sqrt(n) = 1.96*15/0.1

n = (1.96*15/0.1)^2 = 86436

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