The Required Sample size is 138 . Yes, this number of IQ test Score is a fairly large number.
In the given statements we have , An IQ test is designed such that
the mean of adults ( X bar ) = 100
standard deviations (σ ) = 18
Estimate the mean iq score of statistics students such that the confidence level is 95%
We know the value of Z score for given confidence level 95% is 1.96 .
Margin of error in IQ test = 3
we shall calculate the sample size here.
Using the Margin of error formula,
M.E = Z( √σ ²/n )
where, Z--> z score value
σ --> standard deviations
n ---> sample size
putting all the values in this formula we get ,
3 = 1.96 (√(18)²/n )
=> 3/1.96 = √324/n => (1.5306)² = 324/n
=> n = 324/ 2.342 = 138.29
Hence, the required Sample size is 138 .
To learn more about Sample Size , refer:
https://brainly.com/question/24158610
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Complete question:
An IQ test is designed so that the mean is 100 and the standard deviation is 18 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the sample mean is within 3 IQ points of the true mean. Assume that σ =18 and determine the required sample size using technology.
Then determine if this is a reasonable sample size for a real world calculation.