Download SS 024a – Exam #2 - Department of Statistical and Actuarial Sciences

EXAM CODE: 001
November 17, 2004
Department of Statistical and Actuarial Sciences
University of Western Ontario
SS 024a – Exam #2
Name:
________________________________________
Student Number:
________________________________________
STEP 1: Fill in your name in student number above AND on the scantron.
STEP 2: Fill in the circles on the scantron corresponding to your STUDENT NUMBER
and EXAM CODE (001).
STEP 3: Fill in the circles on the scantron corresponding to your answers.
STEP 4: When time is up, stop writing and remain seated until your exam is collected.
THERE ARE 16 QUESTIONS. EACH CORRECT ANSWER IS WORTH 1
MARK OUT OF A POSSIBLE 16 MARKS. YOU HAVE 50 MINUTES.
NO EXTRA TIME WILL BE GIVEN TO FILL IN YOUR SCANTRON.
GOOD LUCK!!!
z
Here are some formulas that may be useful:
x

n
,
1.
How are statistics and parameters related?
(A)
(B)
(C)
(D)
A population parameter estimates a sample statistic.
A sample parameter estimates a population statistic.
A sample statistic estimates a population parameter.
A population statistic estimates a sample parameter.
x  z*

n
,
 z * 
n

 m 
2. A class contains 26 students which are labeled as 1, 2, 3, ..., 26 for the sake of
simplicity. Seven students will be selected to go on a field trip using a simple random
sample. Selection will be done according to lines 132 and 133 of Table B of Random
Digits of your textbook which has been reproduced here:
68732 55259 84292 08796 43165 93739 31685 97150
45740 41807 65561 33302 07051 93623 18132 09547
Which students get to go on the field trip?
(A)
(C)
4, 7, 13, 16, 18, 20, 25
2, 3, 5, 6, 7, 8, 9
(B)
(D)
25, 20, 16, 18, 13, 19, 23
20, 25, 21, 3, 10, 18, 15
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EXAM CODE: 001
November 17, 2004
3. A sample of 12 observations is drawn from a population having a mean of 72 and a
standard deviation of 8. The possible sample means that could be obtained in repeated
sampling have an average value of _____ with a standard deviation of _____ .
(A) 72, 0.82
(C) 72, 0.67
(B) 72, 2.31
(D) We cannot say because of the small sample size.
4. An efficiency expert wishes to determine the average time that it takes to drill three
holes in a certain metal clamp. How large a sample will he need to be 99% confident that
his sample mean will be within 15 seconds of the true mean? Assume that it is known
from previous drilling studies that the standard deviation is  = 40 seconds.
(A) 7
(B) 48
(C) 47
(D) 56
5.
An observed effect is considered statistically significant if…
(A)
(B)
(C)
(D)
…it is so large that it would rarely occur by chance.
…it is the largest among all the possible effects that could happen.
…the effect is considered by the investigator to be important more often than not.
…the effect occurs often.
6. A bank has six tellers available to serve customers. The number of tellers busy with
customers at 1:00 p.m. varies from day to day and depends on chance. The probability
distribution for this random variable is given in the table below. Note that there are 2
missing values.
Number of
busy tellers (X)
0
1
2
3
4
5
6
Probability
P(X)
0.029
0.049
0.078
0.155
0.212
?
?
What is the probability that there are at least three tellers busy?
(A) 0.844
(B) 0.155
(C) 0.689
(D) There is not enough information given.
7. Craps is a game of chance played by rolling two dice and observing the sum of the
faces. If you roll a sum of 7 or a sum of 11 on your first throw, you win automatically.
What is the probability you win on your first throw?
(A) 18/36
(B) (6/36) x (2/36)
(C) 4/36
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(D) 8/36
EXAM CODE: 001
November 17, 2004
8. The weight of the eggs produced by a certain breed of hen is normally distributed
with mean 65 grams and standard deviation 5 grams. Think of cartons of eggs as simple
random samples of size 12 from the population of all eggs. If you purchase one carton of
eggs, what is the probability that the average weight of the eggs in the carton is less than
63 grams?
(A) 0.0823
(B) 0.9162
(C) 0.3446
(D) 0.6554
9. A group of college students believes that herbal tea has remarkable restorative powers.
To test their theory, they make weekly visits to a local nursing home visiting with
residents, talking with them, and serving them herbal tea. After several months, many of
the residents are more cheerful and healthy. The explanatory variable in this experiment
is…
(A)
(B)
(C)
(D)
…the fact that this is a local nursing home.
…herbal tea.
…the emotional state of the residents.
…visits of the college students.
10. Refer to the previous question. The lurking variable in this experiment is…
(A)
(B)
(C)
(D)
…the fact that this is a local nursing home.
…herbal tea.
…the emotional state of the residents.
…visits of the college students.
11. I am interested in estimating the average enrolment at all Canadian universities and
colleges. I have reason to believe that enrolment may differ significantly for each
province. Because of this belief, I draw simple random sample of 2 universities/colleges
from each of the 10 provinces. I then measure the enrolment at each institution in the
sample. My final sample of 20 institutions is…
(A) …a stratified sample.
(C) …a simple random sample.
(B) …a multistage sample.
(D) …a volunteer sample.
12. Consider a 90% confidence interval for the population mean . We took 1000
samples from the population and calculated a 90% confidence interval from each sample.
Which of the following statements is TRUE?
(A) About 900 of the intervals will contain the sample mean.
(B) We are 90% confident that about 900 of the intervals contain the population mean.
(C) Approximately 100 of the intervals will not contain the population mean.
(D) We are 90% confident that exactly 900 of the intervals will contain the population
mean.
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EXAM CODE: 001
November 17, 2004
13. A survey of 359 cars parked in student and faculty parking lots at UWO classified
the brands by country of origin, as seen in the following two-way table:
STUDENT
FACULTY
TOTAL
107
12
55
174
105
33
47
185
212
45
102
359
NORTH AMERICAN
EUROPEAN
ASIAN
TOTAL
Consider the following 4 statements:
(I)
(II)
(III)
(IV)
Less than one-third of cars in the sample were Asian brands.
Over half of the cars in the population belong to faculty members.
The conditional distribution for students is given by 48.5%.
The marginal distribution of brand is given by 59.1%, 12.5%, 28.4%.
Based on the 4 statements above, which one of the following choices is TRUE?
(A)
(B)
(C)
(D)
(I) and (II) are correct.
(I), (II) and (IV) are correct.
(I), (III), and (IV) are correct.
(I) and (IV) are correct.
14. The university administration is interested in estimating the average amount of
money that first year students spend on class books in their first semester. They selected
a random sample of 36 undergraduate students from all first year students at UWO, and
they were asked “How much did you spend on class books this semester?” The answers
they obtained from these students had an average of $343. Assume the population
variance for the amount spent is known to be $484. A 97% confidence interval for the
true average spent on books by first year students in their first semester is given by:
(A) 343  1.33
(B) 343  175.05
(C) 343  7.96
(D) 343  29.17
15. Consider a 95% confidence interval constructed from sample of 250 observations for
a population mean  from a population with  = 14. If we increase the sample size to
1000 observations but hold everything else constant, how will the length of the
confidence interval be affected?
(A)
(B)
(C)
(D)
The length of the interval will be one quarter its original length.
The length of the interval will be one half its original length.
The length of the interval will be twice its original length.
The length of the interval will be four times its original length.
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EXAM CODE: 001
November 17, 2004
16. A graduate student in psychology is doing a research project that explores drug use
among undergraduate students at UWO. She takes a simple random sample of 1000
students and personally interviews each student, asking them each several questions. One
of the questions she asks is “Have you ever used cocaine?” and several students answered
“No.” to this question even though they really had used cocaine. This is an example of…
(A) …non-response bias.
(C) …response bias.
(B) …poor question wording.
(D) …under coverage bias.
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