Transcript Click here for the answers - APStats by Vealey

A study is being conducted to compare the
effectiveness of two medications to reduce
cholesterol levels in adults. It is known that the
medications are more effective on men. Design
an experiment, including a control, for 42
subjects, 21 men and 21 women for testing the
effectiveness of these two medications.
a. Identify the experimental subjects, the factor(s) and its
levels, and the response variable.
b. Explain how you will design the study and include a diagram
of your design. Provide a brief rational for your choice of
design.
c. Explain how you will use randomization and complete the
randomization using the random number table starting at
line 14
A study is being conducted to compare the
effectiveness of two medications to reduce
cholesterol levels in adults. It is known that the
medications are more effective on men. Design
an experiment, including a control, for 42
subjects, 21 men and 21 women for testing the
effectiveness of these two medications.
a.
Identify the experimental subjects, the factor(s) and its
levels, and the response variable.
subjects – 42 adults (21 men & 21 women)
factor(s) – medication
levels – 3 levels (2 different meds & control)
response variable – effectiveness of medications
b. Explain how you will design the study and include a diagram of your
design. Provide a brief rational for your choice of design.
First I would separate the men and women so that I can block for
gender. Then I can compare the results for each gender, as well as
the whole group. Then I would randomly assign the 21 subjects into
three groups. The three levels of treatment would be assigned
randomly to the groups. After a period of time I would measure
the effectiveness of the drug. The diagram shows the portion for
the men’s block. A nearly identical one would be for the women.
This experiment should be repeated to ensure that the results are
typical.
Group 1
(7 men)
21 men,
Group 2
Randonly
assigned
(7 men)
Group 1
(7 men)
Randomly assign
levels of treatment
Apply
med. 1
Apply
med. 2
Apply
placebo
Compare
effectiveness
c.
Explain how you will use randomization and complete the
randomization using the random number table starting at
line 14
Starting at line 14, I would look at 2 digits at a time for the men,
numbered from 01 to 21. The first seven I encounter will form
group 1, the second seven I encounter will from group 2. The
remaining subjects will form group 3. Then I would roll a
number cube to assign each group a treatment.
group 1: 14, 07, 02, 15, 13, 18, 20
group 2: 21, 12, 17, 19, 05, 01, 09
group 3: 03, 04, 06, 08, 10, 11, 16
I would then repeat the process starting for women, starting
where I ended for men.
Remember the 4 principle of Experimental Design:
Control, Randomization, Replication and Blocking. This is an example
of blocking.)
A new weight loss supplement is to be tested at three
different levels (once, twice and three times a day). It is
suspected that gender may play a role in weight loss with
this supplement. Design an experiment, including a
control group for 80 subjects (half of whom are men).
Your answer should include a diagram and an explanation.
Be sure to include how you will do randomization.
This problem is very much like the last one, but there
would be 4 groups of 10 men and 4 groups of 10 women.
Also there are 4 levels: once a day, twice a day, three
times a day and control (none). A placebo would need to
be used in order to have a blind experiment.
95% of the sneakers manufactured by a shoe company have no
defects. In order to find the 5% that do have defects, inspectors
carefully look over every pair of sneakers. Still, the inspectors
sometimes make mistakes because 8% of the defective pairs pass
inspection and 1% of the good ones fail the inspection.
a. Incorporate these facts into a tree diagram.
b. What percent of the pairs of sneakers pass inspection? .9445
c. If a pair of sneakers passes inspection, what is the probability
that it has a defect? .004/.9445 =.0042
.99
pass
NP .9405
No defects
.
.95
.01
.08
.05
fail
NF .0095
pass
DP .004
fail
DF .046
Defects
.92
A researcher suspected a relationship between people’s preferences in movies
and their preferences in pizza. A random sample of 100 people produced the
following two-way table:
Favorite Movie
Pepperoni
Veggie
Cheese
Zorro
20
5
10
35
Chicken Little
8
15
12
35
Dreamer
15
2
13
30
43
22
35
100
a. Fill in the marginal distributions for this table.
b. What percent of these people prefer pepperoni pizza? 43/100 =.43
c. What percent of people who prefer veggie pizza like Zorro? 5/22=.2272
d. What percent of those who like Chicken Little prefer cheese pizza?
12/35 = .3429
Suppose that 80% of a university’s students favor abolishing
evening exams. You ask 10 students chosen at random what their
opinion is on this matter. What is the likelihood that all 10 favor
abolishing evening exams?
a. Describe how you would pose this question to 10 students
independently of each other. How would you model the procedure?
I would collect a list of all the university’s student id numbers.
Then I would use a random number generator to select 10 id
numbers and I would interview those 10 students.
b. Assign digits to represent the answers “Yes” and “No.” I would let
0-7 represent yes and 8-9 will represent no.
c. Simulate 25 repetitions, starting at line 29 of Table B. What is
your estimate of the likelihood of the desired result.
7, 2, 0, 4, 2, 1, 2, ,2 ,8, 7 this is my 1st trial! 9 students favor.
When I run 25 trials I find that only, all 10 students favor the
proposal only 4 out of 25 times, about 16% of the time.
Two 6-sided die are rolled 50 times.
1. Is this binomial setting? Justify.
This could be a binomial setting depending on what
you are looking for in each question since you are
performing the experiment 50 times. If there are
only 2 options in the outcome you desire, the
probability of that outcome doesn’t change and if
each roll of two dice is independent.
2. What is the probability of getting exactly 8 sevens in
these 50 rolls
a. With the Binomial Formula
(50!/(8!*42!))(1/6)^8(5/6)^42 = .1510
b. With Calculator
Binompdf(50,1/6,8)=.1510
3. What is the probability of getting at
most 8 sevens in these 50 rolls?
Binomcdf(50,1/6,8)=.5421
3. What is the probability of getting no
12’s in 15 rolls of these die?
n=15
P(12)=1/36
1-P(all 12s)=1-Binompdf(15,1/36,15)≈0
1-(1/12)^15≈0
3. What is the probability of getting the
first 5 on the 6th roll? P(5)=4/36=1/9
(8/9)^5(1/9) =Geometpdf(1/9,6)=.0617
Thirty-five percent of all employees in a large
corporation are women. If 12 employees are
randomly selected, what is the probability that at
least 4 of them are women?
p=.35, n=12, k=4
P(at least 4 women) =1-P(3 women or less)=
1-Binomcdf(12,.35,3) = .6533
The following shows a cumulative frequency chart
for the distribution of scores on a 10-question
intelligence test.
Score
0
1
2
3
4
5
Number
2
6
13
28
44
62
Score
6
7
8
9
10
Number
89
129
178
266
298
a. What is the median of the scores? Med = 9
b. What is the interquartile range of the scores? Any
outliers? Q1=7, Q3=10 IQR = 3,
IQR*1.5 = 4.5, outliers at 0,1,2
a. What is the mean of the scores? Mean = 7.93
b. Does it appear that the scores are approximately normally
distributed? No, there are outliers so the distribution is
not symmetric. These outliers pull the mean down from
near the median.