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# Busn 278 Essay

2713 words - 11 pages

Final Exam
Review Questions
Solutions Guide
You will probably want to PRINT THIS so you can carefully
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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