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Midterm

STAB22H3 Study Guide - Midterm Guide: Scantron Corporation, Pie Chart, Marginal Distribution
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by OneClass2540294
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Fall 2018

Department
Statistics
Course Code
STAB22H3
Professor
All
Study Guide
Midterm

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University of Toronto Scarborough
STAB22 Midterm Examination
March 2009
For this examination, you are allowed one handwritten letter-sized
sheet of notes (both sides) prepared by you, a non-programmable,
non-communicating calculator, and writing implements.
This question paper has 15 numbered pages; before you start,
check to see that you have all the pages. There is also a signature
sheet at the front and statistical tables at the back.
This examination is multiple choice. Each question has equal
weight. On the Scantron answer sheet, ensure that you enter your
last name, first name (as much of it as fits), and student number
(in “Identification”).
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.)
Before you begin, 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.
Also before you begin, complete the signature sheet, but sign it
only when the invigilator collects it. The signature sheet shows
that you were present at the exam.
1
This is the Pink version. If you did another version, all the questions you did are in here somewhere.
Correct answers are marked by an asterisk, with brief explanation.
1. A random sample of 25 blood donors was given a blood test to determine their blood type. The pie
chart below shows the distribution of the blood types of these 25 donors. (Note: A, B, O and AB are
the blood types)
How many donors in this sample had blood type A?
(a) 10
(b) 15
(c) * 5
(d) 18
(e) 20
20% of 25.
2. Some researchers have proposed a new treatment for Alzheimer’s disease. They propose to divide their
subjects into two groups; one group gets this new treatment, while the other group gets the standard
treatment. At the end of the study, the quality of life of all the subjects is assessed.
What would you say about this study design?
(a) the researchers didn’t need to have a group of subjects receiving the standard treatment. They
could have obtained equally good results with half the number of subjects.
(b) the researchers could have used available data
(c) * it enables the researchers to see whether the new treatment has more than a placebo effect
(d) this is a case where a comparative experiment is not necessary
(e) there is likely to be a nonresponse bias
The group getting the standard treatment is the control group, and doing a comparative experiment
using a control group is the best way to assess whether a treatment is really effective.
3. In the study of Question 2, suppose that the researchers obtain statistically significant results, with
the new treatment offering a higher average quality of life. Are the researchers entitled to conclude
that the new treatment is a cause of a higher quality of life?
2
(a) yes, because the results come from an observational study
(b) no, because the results come from an observational study
(c) * yes, because the results come from a statistical experiment
(d) no, because the results come from a statistical experiment
It’s an experiment because a treatment was imposed on the subjects. Therefore it can produce evidence
of cause and effect, and because statistically significant results were obtained, it does.
4. Two variables xand yare believed to have a straight-line relationship. We would like to predict y
from x. Minitab tells us this about xand y:
Descriptive Statistics: x, y
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum
x 7 0 7.00 1.63 4.32 1.00 3.00 7.00 11.00 13.00
y 7 0 13.43 1.67 4.43 8.00 10.00 13.00 17.00 21.00
Correlations: x, y
Pearson correlation of x and y = 0.941
P-Value = 0.002
Use this information for this question and the two following.
What is the intercept of the regression line for predicting yfrom x?
(a) 5.3
(b) 6.4
(c) 0.9
(d) * 6.7
(e) 1.0
Slope is (0.941)(4.43/4.32) = 0.96, intercept is 13.43 0.96(7) = 6.7.
5. Using the information given in Question 4, what is the predicted value of ywhen x= 10? The slope
of the regression line is 1.0.
(a) 12.2
(b) 13.4
(c) * 16.7
(d) 7.7
6.7 + (1)(10) = 16.7. Or: x= 10 is higher than average for x, and the correlation is positive, so y
should be higher than average for ytoo. The only alternative that is is 16.7.
6. In Question 4, some information is given about two variables xand y. From the information given,
does it make sense to find the regression line?
(a) No, because xand yhave outliers
(b) * Yes
(c) No, because the correlation is not a good measure of the relationship between xand y
(d) No, because the relationship is not a straight line
You can do a quick 1.5×IQR check to verify that there are no outliers. The correlation is a good
measure of the relationship if it is a straight line, and there is nothing in the output to suggest that a
curve would be better.
3

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Description
University of Toronto Scarborough STAB22 Midterm Examination March 2009 For this examination, you are allowed one handwritten letter-sized sheet of notes (both sides) prepared by you, a non-programmable, non-communicating calculator, and writing implements. This question paper has 15 numbered pages; before you start, check to see that you have all the pages. There is also a signature sheet at the front and statistical tables at the back. This examination is multiple choice. Each question has equal weight. On the Scantron answer sheet, ensure that you enter your last name, rst name (as much of it as ts), and student number (in \Identication"). 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.) Before you begin, 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. Also before you begin, complete the signature sheet, but sign it only when the invigilator collects it. The signature sheet shows that you were present at the exam. 1 This is the Pink version. If you did another version, all the questions you did are in here somewhere. Correct answers are marked by an asterisk, with brief explanation. 1. A random sample of 25 blood donors was given a blood test to determine their blood type. The pie chart below shows the distribution of the blood types of these 25 donors. (Note: A, B, O and AB are the blood types) How many donors in this sample had blood type A? (a) 10 (b) 15 (c) * 5 (d) 18 (e) 20 20% of 25. 2. Some researchers have proposed a new treatment for Alzheimers disease. They propose to divide their subjects into two groups; one group gets this new treatment, while the other group gets the standard treatment. At the end of the study, the quality of life of all the subjects is assessed. What would you say about this study design? (a) the researchers didnt need to have a group of subjects receiving the standard treatment. They could have obtained equally good results with half the number of subjects. (b) the researchers could have used available data (c) * it enables the researchers to see whether the new treatment has more than a placebo eect (d) this is a case where a comparative experiment is not necessary (e) there is likely to be a nonresponse bias The group getting the standard treatment is the control group, and doing a comparative experiment using a control group is the best way to assess whether a treatment is really eective. 3. In the study of Question 2, suppose that the researchers obtain statistically signicant results, with the new treatment oering a higher average quality of life. Are the researchers entitled to conclude that the new treatment is a cause of a higher quality of life? 2 (a) yes, because the results come from an observational study (b) no, because the results come from an observational study (c) * yes, because the results come from a statistical experiment (d) no, because the results come from a statistical experiment Its an experiment because a treatment was imposed on the subjects. Therefore it can produce evidence of cause and eect, and because statistically signicant results were obtained, it does. 4. Two variables x and y are believed to have a straight-line relationship. We would like to predict y from x. Minitab tells us this about x and y: Descriptive Statistics: x, y Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum x 7 0 7.00 1.63 4.32 1.00 3.00 7.00 11.00 13.00 y 7 0 13.43 1.67 4.43 8.00 10.00 13.00 17.00 21.00 Correlations: x, y Pearson correlation of x and y = 0.941 P-Value = 0.002 Use this information for this question and the two following. What is the intercept of the regression line for predicting y from x? (a) 5:3 (b) 6.4 (c) 0.9 (d) * 6.7 (e) 1.0 Slope is (0:941)(4:43=4:32) = 0:96, intercept is 13:43 0:96(7) = 6:7. 5. Using the information given in Question 4, what is the predicted value of y when x = 10? The slope of the regression line is 1.0. (a) 12.2 (b) 13.4 (c) * 16.7 (d) 7.7 6:7 + (1)(10) = 16:7. Or: x = 10 is higher than average for x, and the correlation is positive, so y should be higher than average for y too. The only alternative that is is 16.7. 6. In Question 4, some information is given about two variables x and y. From the information given, does it make sense to nd the regression line? (a) No, because x and y have outliers (b) * Yes (c) No, because the correlation is not a good measure of the relationship between x and y (d) No, because the relationship is not a straight line You can do a quick 1:5 IQR check to verify that there are no outliers. The correlation is a good measure of the relationship if it is a straight line, and there is nothing in the output to suggest that a curve would be better. 3
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