STAT 13
(Sec. 1a-1c)
Introduction to Statistical Methods for the Life and Health Sciences
Instructor: Ivo Dinov, Asst. Prof.
Departments of Statistics & Neurology
HOMEWORK 6
Due Date:
Friday, Feb. 28, 2003, turn in after lecture
See the
HW submission rules.
On the front page include the following
header.
-
(HW_6_1) Fluctuations in the market price of precious metals,
such as gold, have been empirically shown to be well approximated by a
Normal
distribution when observed over short intervals of time. In a particular
month, the daily price of gold (for 100g) was believed to have a mean
of $1250 and a standard deviation of $28. A manufacturing jeweler
will use 400g of gold during that particular month. She places the orders
for the gold at the Monday prices each week. She wants to compare the differences
in two different plans for buying the gold.
Plan 1: Buy all 400g on the first Monday at the start
of the month.
Plan 2: Buy 100g of gold on each of the 4 Monday's of
that month.
She has budgeted $5100 to buy the gold. Let T1 be the
total amount paid for the gold using plan 1 and T2 be the
total amount paid for the gold using plan 2.
- Give an appropriate model (including parameters) for the distribution of
T1 .
-
Give an appropriate model (including parameters) for the distribution of
T2 .
-
How do the two models above differ?
-
What is the probability of spending more than the budgeted amount using
plan 1?
-
What is the probability of spending more than the budgeted amount using
plan 2?
-
Which plan appears to be safer?
-
(HW_6_2) Five fair, but unusual, octahedral (8 face) dice
are rolled twice. Let Y be the random variable representing
the total sum from this experiment (each die turns up an integer value
between 1 and 8). Find the expected value of Y,
mY,
and the standard deviation of Y,
sY. Suppose,
we carry this experiment (rolling five dice twice) 9 times. What would
be approximately the distribution of the sample average, Y¯?
What are the mean and the standard deviation of the sample
average? [Note: Not all types of dice, any number of faces, are possible.
For a nice description of which ones that are possible see
the following
web-page.]
-
(HW_6_3) One of the oldest mnemonic techniques is known as
the method of loci. Past experience suggests this method
could be a useful technique for students who want to be able to remember
an ordered set of points for an essay type question in an exam. The first
step in this technique is to think of a set of locations that are naturally
ordered. For example the route you commonly use to get from home to UCLA.
Along this route are various familiar locations such as the bus stop where
you catch the bus. You will require as many familiar locations as the number
of points you wish to remember. The next step is to associate (in
order) each location with one item you wish to remember. When you need
to recall the points simply travel (in your mind) along the route, retrieving
each item as you reach its location.
An experiment with two methods of instruction (normal
and mnemonic) was conducted to evaluate the mnemonic method.
Thirty-nine
participants
were randomly assigned to one of the two methods. Nineteen were
given 24 words and instructed simply to "try and remember" each so that
they could later recall the words (Normal controls). The second
group of 20 participants studied the same 24 words but were instructed
in the method of loci (Mnemonic group). One day later, participants
were tested by being asked to recall the list of 24 words. The response
measured was the number of words correctly recalled out of 24. The results were as follows:
| Controls: |
9 |
7 |
5 |
9 |
7 |
5 |
11 |
7 |
9 |
10 |
15 |
13 |
13 |
8 |
7 |
12 |
12 |
7 |
17
|
|
| Mnemonic
group: |
11 |
14 |
14 |
16 |
12 |
16 |
9 |
13 |
14 |
15 |
17 |
15 |
14 |
20 |
14 |
15 |
14 |
16 |
13 |
10 |
-
What are the mean and standard deviation for the group of participants
who received mnemonic instructions? How about the mean and standard deviation
for the group of participants who received normal instructions?
-
Find a 95% confidence interval for the difference in the mean number
of words recalled between the normal and mnemonic instruction methods.
Interpret your result using plain English in 1-2 sentences.
-
What sample-size would yield a CI of half the size you found above?
-
Does your confidence interval above contain the true difference? Explain
your answer briefly using plain English in 2-3 sentences.
Last modified on
by 
.
Ivo D. Dinov, Ph.D., Departments of Statistics and Neurology,
UCLA School of Medicine