(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/