Question

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?

Answer 1

Answer:

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