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

Phoenix Marks

5 June, 06:50

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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Lucian Huffman · 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