Exam

Premium

Department

Statistics

Course Code

STAB22H3

Professor

All

Study Guide

Midterm

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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