## STAT 110A

(Sec. 3)

Applied Statistics

## Instructor: Ivo Dinov, Asst. Prof.

Departments of Statistics & Neurology
 http://www.stat.ucla.edu/~dinov/

Due Date:

# Friday, May 24, 2002, turn in after lecture

Please, turn in your homework on the due date. See the HW submission rules. On the front page include the following header.

• (HW_5_1)   This data set contains the weights of 100 newly minded US coins (pennies), measured by an extremely accurate instrument.
• What are the sources of variation for these data? Would
• Construct a 90% Confidence Interval (CI) for the population mean. Identify the population of interest. Interpret the CI.
• Construct a 90% Prediction interval (PI) for the weight of another coin. How do the CI and the PI compare?
[Note: In the case you still do not feel comfortable using STATA for this problem, after having Helen (TA) show you the basic commands, you may opt to do the intervals by hand using the first 6 observations.]

• (HW_5_2)  An arthritis drug manifacturer claims a new drug they made aliviates joints discomfort. In a controlled experiment 250 randomly selected arthritis patients are recruited for a study. 150 are assigned to the treatment and 100 to the control (placebo) group. Six months after begining the treatment ptocess the follwing results were obtained. Use confidence intervals to evaluate the manifacturer's claim that the drug is an effective pain reliever for arthritis patients. Make recommendations based on your analysis.
 Improived No Improvement Total # Treatment Group (drug) 100 150 150 Control (placebo) 60 40 100

• (HW_5_3)  Show that for 0<=p<=1, p(1-p) <=0.25.  Then argue that if Y~Binomial(N, p), then Var(Y) <=n/4.

\Ivo D. Dinov, Ph.D., Departments of Statistics and Neurology, UCLA School of Medicine/