Polytechnic Institute of NYU
MA 2054 Sample Final May , 2012
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Directions: You have 120 minutes to answer the following questions. You must show
all your work as neatly and clearly as possible and indicate the final answer clearly. You
may use only a TI-30 calculator. The last page contains formulas that you might find
useful. You may tear that page out.
If you are feeling ill you should inform the proctor. The proctor will note your name, Poly
ID and accept any written statement(s) that you may wish to make regarding your illness.
Problem Possible Points
1
2
3
4
5
6
7
8
Total 100
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(1) (Page 742, 11.83-11.84) The following set of 25 scores was randomly selected from
a teacher’s class list. Let x be the prefinal average and y be the final examination
score. Show all your work. Also, you are given:∑
x = 1865
∑
y = 1563
∑
x2 = 142771
∑
y2 = 99019
∑
xy = 118392
Stu- x y Stu- x y Stu- x y Stu- x y Stu- x y
dents dents dents dents dents
1 75 64 6 66 61 11 64 52 16 71 62 21 59 49
2 86 65 7 55 48 12 76 63 17 86 71 22 81 71
3 68 57 8 84 67 13 71 66 18 71 55 23 58 58
4 83 59 9 61 59 14 73 62 19 96 72 24 90 67
5 57 63 10 68 56 15 78 66 20 96 75 25 92 75
(a) Find the equation of the best line fit.
(b) Calculate the linear correlation coefficient, r.
(c) Test the significance of r at α = .10
(d) Set a 95% confidence interval for ρ.
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(2) You do not need to show your work.
(a) (Page 665, 12.5) Suppose the the number of data 25 is divided into 5 equal
classes (or levels or groups). The ANOVA techniques allow us to test the null
hypothesis (all means are equal) against the alternative hypothesis (at least
one mean is different) with a specific value of α by using the F-distribution
and an F-test statistic, F∗ given by
F∗ =
MS(factor)
MS(error)
.
Fill in the missing information in the ANOVA Table
Source df SS MS F∗
Factor 13.25
Error 4.2
Total
(b) (Page 622 graph, 11. 6) Find the critical values corresponding to the shaded
area using the notation χ?(df, α) with α = .01 and n = 10.
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(3) (Page 533, Question 158) Twenty-four oat-producing counties were randomly se-
lected from across Minnesota for the purpose of testing the claim “The mean oat
crop yield rate is greater than 60 bushels per acre.”. For each county identified, the
yield rate, in bushels of oats per harvested acre, was obtained. The resulting data
are listen below. Show all your work.
56 31 80 53 39 59 63 67 56 66 61 48
46 73 85 77 78 72 63 71 77 81 63 53
(a) What assumptions are you making? Are the assumptions satisfied? Justify.
(b) Calculate the sample mean.
(c) Complete the test using α = .05.
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(4) (Concepts) Determine whether the statements are True or False. You do need to
explain.
(a) The standard deviation of the data set 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 is 3.
(b) Correlation analysis is a method to determine the linear relationship between
two variables.
(c) If A and B are mutually exclusive events, the sum of their probability must
less or equal to one.
(d) Whenever the slope of the regression line is zero, the correlation coefficient will
also be zero.
(e) Correlation coefficients range between 0 and 1.
(f) z(0.5) = 1.
(g) P (z < 1.53) = 0.5 + P (z > 1.53).
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(5) (Page 263, Question 162) A coin A is loaded in such a way that P (heads) = .6 and
a coin B is a balance one. Both coins are tossed. Show all your work.
(a) Find P (both show heads).
(b) Find P (exactly one head shows).
(c) Find the probability that neither coin shows head.
(d) Find the probability that both show heads given that the coin B shows a head.
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(6) (Page 468, Question 192) From a population of unknown mean µ and a standard
deviation σ = 5.0, a sample of size 100 is selected and the sample mean is 40.6.
(a) Determine 95% confidence interval for µ.
(b) complete the hypothesis test involving Ha : µ 6= 40 with α = .05.
(7) True or False questions.
(Chapter Practice Test Part I in Homework 1-7).
(8) This is just a similar format of final exam. Studying from past or sample exams is
NOT recommended. If you do, it should be only AFTER you know how to do all
of the homework questions and examples from the lectures by yourself.
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