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

a) to test  medication affect intelligence  the null and alternative hypotheses are

Ho : = 100

H1 :   100

b) Here we uses the standard normal (Z ) test because sample size n 30 and population standard deviation is known .

c) test statistic

Z = (xbar -) /(/n )

Z = (105 - 100 )/( 15/30)

Z = 1.83

p-value for Z =1.83 and two tailed test

p-value = 2* P( Z > 1.83)

p-value =2* 0.0336 =0.0673

Decision rule : Reject Ho if p-value < , otherwise fail to reject Ho

p-value = 0.0673 > 0.05

Decision : We reject the null hypothesis Ho

conclusion : There is no sufficient evidence to support the claim that  medication affect intelligence

d) 95% confidence interval for

xabr - Z_a/2*(/n ) < < xbar + Z_a/2 *(/n)

for a= 0.05

Z_0.025 = 1.96

105 - 1.96*(15/30) < < 105 + 1.96 *(15/15)

99.63 < < 110.37

We are 95% confident that true mean IQ lies between in this interval.