Statistics

Name: _________________________

Please complete the following exercises/problems. The due date is listed on the syllabus (typically the next class period). Remember to
SHOW ALL WORK
to receive full credit. Use the back and attach additional sheets as needed.

Let’s say we are interested in the effect of a new intelligence enhancing drug known as NZT-47, on IQ. We already know the population mean and standard deviation for IQ scores (μ = 100, σ = 15), and the scores are normally distributed. We take a sample of 30 individuals and administer the drug. The sample’s mean IQ score after taking the drug is 180. Answer the following questions based on this scenario:

1. What is the raw score effect size for the effect of the drug?

2. What is the standardized effect size (Cohen’s d) for the effect of the drug?

3. Would you classify this as small, medium, or large?

We refine the drug and create NZT-48. Based on the enhancements we have made, we believe that administering the new NZT will increase IQ by 120 points. We want to use a sample size of n = 5. The parameters of the untreated population remain the same (μ = 100, σ = 15, normally distributed). Answer the following questions based on this scenario:

1. What is the mean of the null distribution?

2. What is the mean of the research distribution?

3. What is the shape of the null distribution?

4. What is the shape of the research distribution? How do you know?

5. What is the standard error for these distributions?

6. Use a one-tailed test with an alpha of .05. What is your cut-off score on the null distribution?

7. What raw score does the above cut-off z correspond to on the null distribution?

8. Convert that raw score to a z-score on the research distribution.

9. How much power do you have to detect the hypothesized 120-point effect of NZT-48?