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Final Exam

Review Questions

Solutions Guide

You will probably want to PRINT THIS so you can carefully

check your answers. Be sure to ask your instructor if you have

questions about any of the solutions given below.

1. Explain the difference between a population and a sample. In

which of these is it important to distinguish between the two in order

to use the correct formula? mean; median; mode; range; quartiles;

variance; standard deviation.

Solution: A sample is a subset of a population. A population consists

of every member of a particular group of interest. The variance and

the standard deviation require that we know whether we have a

sample or a population.

2. The following ...view middle of the document...

5 means moderate positive correlation

etc.

7. Does correlation imply causation?

Solution: No.

8. What do we call the r value.

Solution: The correlation coefficient.

9. To predict the annual rice yield in pounds we use the equation

ˆ

y = 859 + 5.76 x1 + 3.82 x2 , where x1 represents the number of acres

planted (in thousands) and where x2 represents the number of acres

harvested (in thousands) and where r2 = .94.

a)

Predict the annual yield when 3200 acres are planted and 3000

are harvested.

b)

Interpret the results of this r2 value.

c)

What do we call the r2 value?

Solution:

ˆ

(a) y = 859 + 5.76*3200 + 3.82*3000

= 859 + 18432 + 11460

= 30751 which is 30,751,000 pounds of rice

(b) 94% of the variation in the annual rice yield can be explained by

the number of acres planted and harvested. The remaining 6% is

unexplained and is due to other factors or to chance.

(c) It is the coefficient of determination.

10. The Student Services office did a survey of 500 students in which

they asked if the student is part-time or full-time. Another question

asked whether the student was a transfer student. The results follow.

Transfer Non-Transfer Row Totals

Part-Time

100

110

210

Full-Time

170

120

290

Column Totals 270

230

500

a) If a student is selected at random (from this group of 500

students), find the probability that the student is a transfer student. P

(Transfer)

b) If a student is selected at random (from this group of 500

students), find the probability that the student is a part time student.

P (Part Time)

c) If a student is selected at random (from this group of 500

students), find the probability that the student is a transfer student

and a part time student. P(transfer ∩ part time).

d) If a student is selected at random (from this group of 500

students), find the probability that the student is a transfer student if

we know he is a part time student. P(transfer | part time).

e) If a student is selected at random (from this group of 500

students), find the probability that the student is a part time given he

is a transfer student. P(part time | transfer)

f) Are the events part time and transfer independent? Explain

mathematically.

g) Are the events part time and transfer mutually exclusive. Explain

mathematically.

Solution: (a) The total number of transfer students is 270. The total

number of students in the survey is 500. P(Transfer) = 270/500 = .54

(b) The total number of part time students is 210. The total number

of students in the survey is 500. P(Part Time) = 210/500 = .42

(c) From the table we see that there are 100 students which are both

transfer and part time. This is out of 500 students in the sample.

P(transfer ∩ part time) = 100/500 = .20

(d) This is conditional probability and so we must change the

denominator to the total of what has already happened. There are

100 students which are both transfer and part time. There are 210

part time...

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