Question

HW10: Power Analysis and Sample size

INSTRUCTIONS: Please find the sample size that would allow the graduate student below to draw a conclusion with 95% confidence and a power level of 0.85.

Scenario: A graduate student has administered a pro-inflammatory substance, lipopolysaccharide (LPS), to humans in the form of a pill (2 doses – 0mg or placebo and 15mg; n=35 patients per group). She then determines the blood concentration (in pg/ml) of a particular protein that is known to be upregulated due to LPS called Inflammotin using ELISA (hint: pick the correct test – remember the power table depends on the alpha value and the test type). The effect size (difference in population means) she would like to detect is 70 pg/ml of Inflammotin and the population standard deviation (estimated from a pilot study) for both groups is 100 pg/ml of Inflammotin.

1. (10 points)What is α? __________________________________
2. (10 points)What is β? __________________________________
3. (10 points)What is the appropriate test? _____________________________________________________________
4. (25 points)What is the normalized difference? (Show work.)
5. (25 points)What is the appropriate sample size (or number of sample per group) that would allow us to draw conclusions about the aforementioned experiment with 95% confidence and a power level of 0.85? ______________________________________________
6. (20 points)Has the graduate student selected the appropriate sample size for our power and confidence criteria? Why or why not? ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ___________________________________________________________________________________________________________________________

Answer 1