HARDMAN MAT 2170 Review for Final Exam

HARDMAN
MAT 2170
Review for Final Exam
1. Know the definitions of the following terms:
A. Margin of Error
B. Mean
C. Range
D. Parameter
E. Continuous
F. Outliers
G. Scatterplot
H. Mutually Exclusive
I. Statistic
J. IQR
K. Median
L. Correlation
M. Sample Space
N. Standard Deviation
O. Independent
P. Quartiles
Q. Boxplot
R. Event
S. Discrete

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2. DRAW THE APPROPRIATE PICTURES, and calculate each of the following
probabilities. (3 points each)
a.

P [ 1.33 ≤ T ( 17) ≤ 2.567 ]

b.

P [ 0.61< Z <2.39 ]

3. Suppose that X~Bin(12, 0.4):
a. Calculate the probability that X = 8

b. Calculate

P [ 5< X ≤ 8 ]

(5 points)

(5 points)

4. Assume that you will take a sample of size 36 from a population of GPAs with a
mean value of 2.1 and a population standard deviation of 0.4.
a. Specify the sampling distribution of

b. Calculate

´ >2.20 ] . (4 points)
P[X

X´ , your sample mean value. (6 points)

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5. Suppose that you do know the value of the population standard deviation and that you
want to calculate an 80% CI for μ , the population mean value. Determine the
value of
the critical number that you would use to calculate this CI. (4 points)

6. Given the following probability distribution table for the random variable X:
X: -3
f(x): 0.3

2
0.5

7
0.2

a. Calculate the Expected Value of X. (6 points)

b. Calculate the Variance of X. (6 points)

7. Given the following heights measured in inches: 68, 72, 65, 69, 72:
a. Calculate the mean height for this sample. (2 points)

b. Calculate the standard deviation for this sample of heights. (4 points)

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8. Suppose that you will pick two cards from a standard deck of 52 cards, without
replacement, and you are only interested in whether each of the cards that you select
is a diamond, or not.
a. Draw the complete tree diagram, with all of the twig probabilities in place. (5 pts)

b. What is the probability that exactly 1 of the two cards that you select is a
diamond? (5 points)

9. Use the data set in question 7 to find the 95% CI for

μ . (6 points)

10. Name the two desirable properties for any CI. (4 points)

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11. Students were given a quiz, and the amount of time (measured in minutes) it took
each student to finish the quiz was recorded. The results follow:
10, 11, 11.25, 12.5, 12.5, 14, 15, 18, 18, 20, 22
a. Complete the 5-Number summary of this data set: (3 points)
Min: _______
Q1: _______
Q2: _______
Q3: _______
Max: _______
b. Calculate the IQR for this data set. (2 points)

c. Calculate the Upper Fence for this data set. (2 points)

d. What is the reason that you would calculate the Fences in an analysis? (2 points)

12. Calculate the sample size required to produce a 90% CI for
an acceptable margin of error, E, is 1.25. (3 points)

μ if σ =14.9 and

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13. Consider the following scatterplots: (3 points each)
6

5

5

4

4

3

3

2

2

1

1

0
0
0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5
5
4
3
2
1
0
0.5 1 1.5 2 2.5 3 3.5 4 4.5

#1

#2

a. Which scatterplot has the smallest r-value?

b.Which scatterplot shows the weakest linear correlation?

c. Which scatterplot has an r-value closest to 1?

#3

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14. Assume that you ran the following hypothesis test:
H O :μ ≥ 98
H A : μ<98
and that you got the following test statistic: Z O =−1.79 .
Calculate the P-Value. (3 points)