University of Toronto Scarborough
STAB22 Final Examination
April 2009
For this examination, you are allowed two handwritten letter-sized
sheets of notes (both sides) prepared by you, a non-programmable,
non-communicating calculator, and writing implements.
This question paper has 17 numbered pages. Before you start,
check to see that you have all the pages. You should also
have a Scantron sheet on which to enter your answers, and a set
of statistical tables. If any of this is missing, speak to an invigilator.
This examination is multiple choice. Each question has equal
weight, and there is no penalty for guessing. To ensure that
you receive credit for your work on the exam, fill in the bubbles
on the Scantron sheet for your correct student number (under
“Identification”), your last name, and as much of your first name
as fits.
Mark in each case the best answer out of the alternatives given
(which means the numerically closest answer if the answer is a
number and the answer you obtained is not given.)
If you need paper for rough work, use the back of the sheets of this
question paper. The question paper will be collected at the end of
the examination, but any writing on it will not be read or marked.
Before you begin, two more things:
• Check that the colour printed on your Scantron sheet matches
the colour of your question paper. If it does not, get a new
Scantron from an invigilator.
• Complete the signature sheet, but sign it only when the in-
vigilator collects it. The signature sheet shows that you were
present at the exam.
1
,1. A simple random sample of 70 coffee drinkers was taken. Each sampled coffee drinker was asked to
taste two unmarked cups of coffee, one of which is actually Brand A and the other is Brand B, and
was asked which one they preferred. 44 coffee drinkers preferred Brand A, and the other 26 preferred
Brand B. Use this information to answer this question and the next one.
The people who commissioned the survey are trying to find out whether a majority of all coffee-drinkers
(that is, more than 50% of them) prefer brand A. Carry out a suitable test of significance to assess the
evidence. What is the P-value of your test?
(a) between 0.05 and 0.10
(b) between 0.025 and 0.05
(c) greater than 0.10
(d) between 0.01 and 0.025
(e) less than 0.01
2. In the situation of Question 1, it turned out that the coffee drinkers had always been given an unmarked
cup containing Brand A coffee first, and Brand B coffee second. How do you react to this knowledge?
(a) The P-value was small, so there will still be good evidence that Brand A is preferred.
(b) The coffee drinkers received their coffee in unmarked cups, so it doesn’t matter which brand is
actually tasted first.
(c) Brand A must have an advantage by being tasted first, so there cannot be a significant difference
between brands A and B.
(d) The P-value was large, so there will still be no evidence that Brand A is preferred.
(e) A better approach would have been to toss a coin to decide whether each drinker gets Brand A
first or Brand B first.
3. A university financial aid office took a simple random sample of students to see how many of them were
employed the previous summer. Of the 750 men sampled, 703 had been employed the previous summer;
of the 650 women sampled, 592 had been employed the previous summer. Use this information for this
question and the next one.
Test whether the proportion of all male students employed last summer is different from the proportion
of all female students employed last summer. What is the P-value of your test?
(a) between 0.05 and 0.10
(b) between 0.01 and 0.025
(c) between 0.025 and 0.05
(d) less than 0.01
(e) greater than 0.05
4. From the information given in Question 3, what is the upper limit of a 95% confidence interval for the
difference between the proportion of men employed the previous summer and the proportion of women
employed the previous summer? (Take the difference as men minus women.)
(a) 0.05
(b) -0.10
(c) 0.10
(d) 0.00
(e) -0.05
2
, 5. A report states that 3% of all births are “multiple births” (that is, twins, triplets, etc.). A random
sample of 5000 births is taken. Assuming the report to be correct, what is the probability that 2.5%
or less of the births in the sample are multiple births?
(a) less than 0.02
(b) between 0.05 and 0.10
(c) greater than 0.30
(d) between 0.02 and 0.05
(e) between 0.10 and 0.30
6. A population has a mildly non-normal shape with mean 35 and standard deviation 7.5. A sample of
size 225 is taken from this population. What is the probability that the sample mean is less than 33.5?
(a) about 0.001
(b) 0.05
(c) 0.42
(d) more than 0.90
(e) 0.12
7. A simple random sample of 30 observations is taken from some population. The sample mean is 120.
You wish to test the null hypothesis µ = 116 against the alternative µ 6= 116, but you have only the
output below.
N Mean SE Mean 95% CI
30 120.000 1.826 (116.422, 123.578)
N Mean SE Mean 99% CI
30 120.000 1.826 (115.297, 124.703)
What can you say about the P-value of your test?
(a) It is less than 0.01.
(b) It is greater than 0.95.
(c) It is less than 0.05.
(d) It is greater than 0.05.
(e) It is less than 0.05 but greater than 0.01.
8. It is desired to estimate the mean of a population using a 95% confidence interval. The population is
known to have a highly skewed shape. A sample of size 45 is proposed. What do you think of this
choice of sample size?
(a) the sample size may not be large enough to allow the Central Limit Theorem to apply
(b) the sample size is bigger than 30, so the calculation should be accurate
(c) the sampling distribution of the sample mean has exactly a normal shape regardless of the shape
of the population
(d) the normal distribution will be an accurate approximation to the t distribution in this case
(e) The Law of Large Numbers says that the sample mean and population mean will be close, so
there is no need to calculate a confidence interval
3
STAB22 Final Examination
April 2009
For this examination, you are allowed two handwritten letter-sized
sheets of notes (both sides) prepared by you, a non-programmable,
non-communicating calculator, and writing implements.
This question paper has 17 numbered pages. Before you start,
check to see that you have all the pages. You should also
have a Scantron sheet on which to enter your answers, and a set
of statistical tables. If any of this is missing, speak to an invigilator.
This examination is multiple choice. Each question has equal
weight, and there is no penalty for guessing. To ensure that
you receive credit for your work on the exam, fill in the bubbles
on the Scantron sheet for your correct student number (under
“Identification”), your last name, and as much of your first name
as fits.
Mark in each case the best answer out of the alternatives given
(which means the numerically closest answer if the answer is a
number and the answer you obtained is not given.)
If you need paper for rough work, use the back of the sheets of this
question paper. The question paper will be collected at the end of
the examination, but any writing on it will not be read or marked.
Before you begin, two more things:
• Check that the colour printed on your Scantron sheet matches
the colour of your question paper. If it does not, get a new
Scantron from an invigilator.
• Complete the signature sheet, but sign it only when the in-
vigilator collects it. The signature sheet shows that you were
present at the exam.
1
,1. A simple random sample of 70 coffee drinkers was taken. Each sampled coffee drinker was asked to
taste two unmarked cups of coffee, one of which is actually Brand A and the other is Brand B, and
was asked which one they preferred. 44 coffee drinkers preferred Brand A, and the other 26 preferred
Brand B. Use this information to answer this question and the next one.
The people who commissioned the survey are trying to find out whether a majority of all coffee-drinkers
(that is, more than 50% of them) prefer brand A. Carry out a suitable test of significance to assess the
evidence. What is the P-value of your test?
(a) between 0.05 and 0.10
(b) between 0.025 and 0.05
(c) greater than 0.10
(d) between 0.01 and 0.025
(e) less than 0.01
2. In the situation of Question 1, it turned out that the coffee drinkers had always been given an unmarked
cup containing Brand A coffee first, and Brand B coffee second. How do you react to this knowledge?
(a) The P-value was small, so there will still be good evidence that Brand A is preferred.
(b) The coffee drinkers received their coffee in unmarked cups, so it doesn’t matter which brand is
actually tasted first.
(c) Brand A must have an advantage by being tasted first, so there cannot be a significant difference
between brands A and B.
(d) The P-value was large, so there will still be no evidence that Brand A is preferred.
(e) A better approach would have been to toss a coin to decide whether each drinker gets Brand A
first or Brand B first.
3. A university financial aid office took a simple random sample of students to see how many of them were
employed the previous summer. Of the 750 men sampled, 703 had been employed the previous summer;
of the 650 women sampled, 592 had been employed the previous summer. Use this information for this
question and the next one.
Test whether the proportion of all male students employed last summer is different from the proportion
of all female students employed last summer. What is the P-value of your test?
(a) between 0.05 and 0.10
(b) between 0.01 and 0.025
(c) between 0.025 and 0.05
(d) less than 0.01
(e) greater than 0.05
4. From the information given in Question 3, what is the upper limit of a 95% confidence interval for the
difference between the proportion of men employed the previous summer and the proportion of women
employed the previous summer? (Take the difference as men minus women.)
(a) 0.05
(b) -0.10
(c) 0.10
(d) 0.00
(e) -0.05
2
, 5. A report states that 3% of all births are “multiple births” (that is, twins, triplets, etc.). A random
sample of 5000 births is taken. Assuming the report to be correct, what is the probability that 2.5%
or less of the births in the sample are multiple births?
(a) less than 0.02
(b) between 0.05 and 0.10
(c) greater than 0.30
(d) between 0.02 and 0.05
(e) between 0.10 and 0.30
6. A population has a mildly non-normal shape with mean 35 and standard deviation 7.5. A sample of
size 225 is taken from this population. What is the probability that the sample mean is less than 33.5?
(a) about 0.001
(b) 0.05
(c) 0.42
(d) more than 0.90
(e) 0.12
7. A simple random sample of 30 observations is taken from some population. The sample mean is 120.
You wish to test the null hypothesis µ = 116 against the alternative µ 6= 116, but you have only the
output below.
N Mean SE Mean 95% CI
30 120.000 1.826 (116.422, 123.578)
N Mean SE Mean 99% CI
30 120.000 1.826 (115.297, 124.703)
What can you say about the P-value of your test?
(a) It is less than 0.01.
(b) It is greater than 0.95.
(c) It is less than 0.05.
(d) It is greater than 0.05.
(e) It is less than 0.05 but greater than 0.01.
8. It is desired to estimate the mean of a population using a 95% confidence interval. The population is
known to have a highly skewed shape. A sample of size 45 is proposed. What do you think of this
choice of sample size?
(a) the sample size may not be large enough to allow the Central Limit Theorem to apply
(b) the sample size is bigger than 30, so the calculation should be accurate
(c) the sampling distribution of the sample mean has exactly a normal shape regardless of the shape
of the population
(d) the normal distribution will be an accurate approximation to the t distribution in this case
(e) The Law of Large Numbers says that the sample mean and population mean will be close, so
there is no need to calculate a confidence interval
3
