Question

In the population, the average IQ is 100 with a standard deviation of 15. A team of scientists wants to test a new medication to see if it has either a positive or negative effect on intelligence, or no effect at all. A sample of 30 participants who have taken the medication has a mean of 105. It is assumed that the data are drawn from a normally distributed population. Did the medication affect intelligence, using α = 0.05?

(a) State hypotheses appropriate to the research question.

(b) Describe what test would you use and state the reasons for your choice.

(c) Draw a conclusion in the context of the problem using the p-value.

(d) Construct a 95% CI for µ. Conclude in the context of the problem.

(e) Compute the power if the true population mean is 110.

Answer 1

b) One should use a one sample z test.

a) Let denotes the average IQ after new medication.

d)