The number of statistics professors selected for 95% confidence in IQ test is 216.
A 95% confidence interval indicates that if we compute a 95% confidence interval for each of 100 independent samples, then about 95 of the 100 confidence intervals will include the real mean value μ.
Formula for Sample Mean M is [tex]M=Z\times\frac{\sigma}{\sqrt{n}}[/tex].
The alpha level is given by,
[tex]\alpha=\frac{1-0.95}{2} \\=0.025[/tex]
Now, finding the z value in the Z table as such z has a p value of 1-α.
So, z with a p value of 1-0.025=0.975, so
Z=1.96
Now, Using the formula of M, the value of [tex]\sigma[/tex] is 15 and M=2,
[tex]M=Z\times\frac{\sigma}{\sqrt{n}}\\2=1.96\times\frac{15}{\sqrt{n}} \\\sqrt{n}=14.7\\n=14.7^2\\n=216.09\\n\approx216[/tex]
Hence, the number of statistics professors will be 216.
Therefore, the number of statistics professors selected for 95% confidence in IQ test is 216.
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The given question is incomplete. Here is the complete question:
Assume that we want to estimate the mean iq score for the population of statistics professors. how many statistics professors must be randomly selected for iq tests if we want 95% confidence that the sample mean is within 2 iq points of the population mean? Assume that the standard deviation of the IQ of statistics professors is σ= 15.