Some IQ tests are standardized based on the assumption that the population mean is 100 and the standard deviation is 15. Test graders decide to reject this hypothesis if a random sample of 25 people has a mean IQ greater than 110. Assuming that IQ scores are normally distributed, what's the power of the test if the true population mean is 105?

Question

Mathematics

Allan Cuevas

25 November, 14:37

Some IQ tests are standardized based on the assumption that the population mean is 100 and the standard deviation is 15. Test graders decide to reject this hypothesis if a random sample of 25 people has a mean IQ greater than 110. Assuming that IQ scores are normally distributed, what's the power of the test if the true population mean is 105?

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Tyree Mcdaniel · Answer 1

0.952

Step-by-step explanation:

we know that

here standard error = std deviation: (n) ^1/2

=15 / (25) ^1/2 = 15/5=3

Assuming that IQ scores are normally distributed

Now, probability of a Type II error

=P (X<110) = P (Z< (110-105) / 3) = P (Z<1.67)

=0.952

the power of the test if the true population mean is 105 = 0.952