Download Stat 31-Sect 3 (Spring 2001) Midterm Exam 2

Stat 31-Sect 3 (Spring 2001) Midterm Exam 2
Date: April 4, 2001
Total Points: 100 Time Allowed: 50 minutes
Instructions: Be sure to show all work and answer questions
completely. You MUST justify your answers. Circle your final answer.
This is a closed book and closed note examination.
Name: _____________________________________
Pledge: I have neither given nor received unauthorized aid during this
exam.
Signature:___________________________________
The first five questions are multiple choice. Circle your answer CLEARLY.
1. One reason for using random allocation to assign units to treatments in an experiment
is
a.
b.
c.
d.
to produce the placebo effect
to produce experimental groups that are similar
to eliminate lack of realism
to produce the blocks in a block design
2. The sampling distribution of a statistic is
a. The probability that we obtain the statistic in repeated random samples
b. The mechanism that determines whether randomization was effective
c. The distribution of values taken by a statistic in all possible samples of the
same size from the same population
d. The extent to which the sample results differ systematically from the truth
3. The probability that Bob plays soccer on any given Saturday is 0.70, and the chance
of rain is 0.25, as on any other day. Given that it is raining, the probability that Bob
plays soccer is only 0.20.What is the chance that Bob plays and it rains on the same
Saturday?
a.
b.
c.
d.
0.175
0.95
0.14
0.05
4. Will a fluoride mouthwash used after brushing reduce cavities? 20 sets of twins were
used to investigate this question. One member of each set of twins used the
mouthwash after each brushing, the other did not. After 6 months, the number of
cavities of those using the mouthwash was compared to the number of cavities of
those not using the mouthwash. The experiment uses
a. random placebos
b. double replication
c. double blinding
d. a matched pair design
5. In order to take a sample of 1200 people from a population, I first divide the
population into men and women, and then take a simple random sample of 500 men
and a separate sample of 700 women. This is an example of a
a. block design
b. stratified random sample
c. double-blind simple random sample
d. randomized comparative sample
6. In a group of students, 45% play golf, 55% play tennis, and 70% play at least one of
these sports. One student in this group is chosen at random.
a.
What is the probability that the student does not play any of these sports?
b. What is the probability that the student plays golf but not tennis?
c. Are playing golf and playing tennis independent events? Explain why.
7. The IRS knows that 25% of all tax reports contain false information. An inspector is
assigned to carefully inspect 6 randomly selected tax returns per day.
a. What will be the mean and standard deviation for the number of tax reports
with false information in a day?
b. What is the probability that the inspector finds that 2 tax reports are false in a
day?
c. What is the probability that the inspector finds that at least 1 is false in a day?
d. In 2 consecutive days (they are independent), what is the probability that for
each day at least 1 is false?
8. An urn contains 200 balls of equal size, weight and texture. There are 150 balls
labeled $0, there are 40 balls labeled $1, and there are 10 balls labeled $5.
Blindfolded, you will randomly pick one ball from the urn, and your prize is the
amount of money indicated on the label of your chosen ball. What is the expected
value and variance of your prize?
9.
An experiment investigated the effects of repeated exposure to an advertising
message using undergraduate students as subjects. All subjects viewed a 40-minute
television program that included ads for a digital camera. Some subjects saw a 30second commercial; others, a 90-second version. The same commercial was repeated
either 1,3, or 5 times during the program. After viewing, all of the subjects were
asked about their recall of the ad.
a. Identify the experimental units or subjects.
b. Identify the factors.
c. Identify the treatments.
d. Identify the response variables.
10. A sociologist is studying the effect of having children within the first two years of
marriage on the divorce rate. Using hospital birth records, she selects a random sample
of 200 couples who had a child within the first two years of marriage. She finds that 80
couples divorced within five years of marriage.
a. Find a 95% confidence interval for the divorce rate (within 5 years) of couples
who have children within the first two years of marriage.
b. In general, half of couples divorce within the first five years of marriage. Do
those that have children within the first two years have a lower divorce rate?
Use a hypothesis test to answer this question, and clearly state your results.
(Use an alpha of 0.05)
11.
a. If X is distributed uniform between 0 and 1, what is P(X<0.6) ?
b. If you generate a column with 10 random numbers with Excel, how would you
calculate P(3 of the 10 numbers generated are less than 0.6)?