Introduction to Statistical Methods for the Life and Health Sciences
Instructor: Ivo Dinov, Asst. Prof.
Departments of Statistics & Neurology
Friday, Feb. 21, 2003, turn in after lecture
HW submission rules.
On the front page include the following
(HW_5_1) The casino game of Tai Sai is played by betting
on various possible combinations of results when three dice are
rolled. One possibility is to place a bet on a single number. In this case,
the more times this number appears on the three dice, the greater the winnings.
Here's an example of how it works: Consider a gambler who wishes
to bet on the number six. For each dollar bet, the player wins twelve
times his/her stake if three sixes are rolled on the three dice, two times
his/her stake if two sixes are rolled on the three dice or one times his/her
stake if only one six is rolled on the three dice. If no sixes are rolled,
then the stake is lost.
Let X be the return from a single bet with a $5 stake. X
has the following probability function:
Compute E[X], SD[X] and the probability of making a positive return
from a single bet.
A player will make a profit overall if their mean return from placing a
series of bets is positive. Let X_bar be the mean return from 100
separate bets with a $5 stake.
What are the values of E[X_bar] and SE[X_bar]?
What is the approximate distribution of X_bar? What theorem was
needed to decide this?
Calculate the probability of, on average, making a positive return from
placing one hundred separate bets with $5 stakes.
Repeat the calculations above using 1,000, 5,000 and 10,000
Create a scatter plot of probability that the mean return from playing
Sai is positive (on y-axis) versus number of bets (on x-axis).
Comment on what the plot appears to show.
(HW_5_2) Successful TV advertising depends on being able to get
viewers to recall the specific brand being advertised. Two groups of randomly
selected students are shown the TV ads for 10 products. One groups saw the
TV ads with some sexual content, the other saw the TV ads rated for general
audience. One week after seeing the ads each students was asked to
name the specific brands which they saw on TV. The mean and SD of the number
of correct answers for each group are given in the table below.
- Calculate SE(X1_bar - X2_bar), the standard error of the differences of the sample means for the two groups
- Calculate the two standard error interval for the difference of the two population means m1 - m2
- Write a one paragraph report summarizing your conclusions from the analysis of these data.
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Last modified on
Ivo D. Dinov, Ph.D., Departments of Statistics and Neurology,
UCLA School of Medicine