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the standard iq test is designed so that the mean is and the standard deviation is for the population of all adults. we wish to find the sample size necessary to estimate the mean iq score of statistics students. suppose we want to be % confident that our sample mean is within iq points of the true mean. the mean for this population is clearly greater than . the standard deviation for this population is probably less than because it is a group with less variation than a group randomly selected from the general population; therefore, if we use we are being conservative by using a value that will make the sample size at least as large as necessary. assume then that and determine the required sample size.

Answer :

If we assume that σ = 15 then the required sample size is 216 .

In the question ,

it is given that ,

the standard deviation is (σ) = 15

we want to be  95% confident . So , α [tex]=[/tex] 1 - 0.95 = 0.05

So , [tex]Z_{\frac{\alpha }{2} }[/tex] is = [tex]Z_{\frac{0.05 }{2} }[/tex] = Z₀.₀₂₅

from z table ,

Z₀.₀₂₅  = 1.96 .

e is given to be = 2 IQ points

the sample size (n) is calculated using the formula .

n = (σ × [tex]Z_{\frac{\alpha }{2} }[/tex]/e)²

Substituting the values ,

we get ,

n = (15 * 1.96/2)²

n = (29.4/2)²

n = (14.7)²

n = 216.09

n ≈ 216

Therefore , the sample size necessary to estimate the mean IQ score of statistics students is 216 .

The given question is incomplete , the complete question is

The standard IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of all adults. We wish to find the sample size necessary to estimate the mean IQ score of statistics students. Suppose we want to be 90% confident that our sample mean is within 2 IQ points of the true mean. Assume then that σ = 15 and determine the required sample size .

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