Math 210 - Exam 5 - Sample Exam

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Math 210 - Exam 5 - Sample Exam
Math 210 - Exam 5 - Sample Exam
1) A researcher claims that the responses occur with percentages of 15%, 20%, 25%, 25%,
and 15% respectively. Below is a sample of responses. If the claim is true, how many
times would you expect the response to be "D"?
Response A B C D E
Frequency 12 15 16 18 19
A) 4.5
B) 6.1
C) 22.3
D) 20
2) A random sample of 4 homes in Dutchess County, New York is taken. The selling price
and the list price of each home is taken. Use the data to obtain a 90% confidence interval
for the mean difference, µd , in the selling price and list price of homes in Dutchess
County.
Home
Selling Price
List Price
A
$377,500
$385,000
B
$268,000
$275,000
A) -7815 < µd < -3885
C) -8508 < µd < -3192
C
$379,000
$383,900
D
$225,000
$229,000
B) -10728 < µd < -971.9
D) -9642 < µd < -2058
3) Ten different families are tested for the number of gallons of water a day they use before
and after viewing a conservation video. Let the differences be D = Before - After.
Determine the alternative hypothesis to test the claim that water usage has decreased.
Before 33 33 38 33 35 35 40 40 40 31
After 34 28 25 28 35 33 31 28 35 33
A) H1: µd < 0
B) H1: µd > 0
C) H1: µd
0
D) H1: µd 0
4) Find the correlation coefficient, r.
x 23.6 35.3 18.3 49.0 13.2
y
4
9
3
3
8
A) -0.178
B) 0
C) -0.2
1
D) 0.2
5) A random sample of cars is taken. The color of the car and whether it was in an accident
was also recorded. Find the critical value needed to test the claim that the row and
column variable ard independent at the 0.01 significance level.
Red Blue White
Car has been in
accident
Car has not been
in accident
A) 9.210
28
33
36
23
22
30
B) 4.605
C) 16.812
D) 10.645
6) 155 students who were majoring in either math or English were asked a test question, and
the researcher recorded whether they answered the question correctly. The sample results
are given below. If the row and column variables are independent, how many in the
sample would you expect to be math majors and answer the question correctly?
Correct Incorrect
Math
22
53
English
43
37
A) 31.45
B) 30.77
C) 29.31
D) 32.14
7) We wish to compare the means of two populations using paired observations. Suppose
that d = 3.125, Sd = 2.911, and n = 8, and that you wish to test H1: µd > 0 at the 0.1 level
of significance. What is the p-value?
A) 1.415
B) 3.036
C) 0.0095
2
D) 2.326
8) A random sample of oceanfront (directly on the beach) and oceanside homes in Long
Beach Island are taken. Use the information below to find the p-value for testing the
claim that the mean price of oceanfront homes is greater than the mean price of oceanside
homes (H1: µOF > µOS).
Sample
Means
Sample
SDs
Sample
Sizes
A) 0.0124
Oceanfront
Oceanside
$2,574,200
$1,036,800
762,561.93
$39995.25
5
5
B) 0.0038
C) 0.0053
D) 0.0275
9) A researcher wishes to determine whether the blood pressure of vegetarians is lower
than the blood pressure of nonvegetarians. Independent simple random samples of 85
vegetarians and 75 nonvegetarians yielded the following sample statistics for systolic
blood pressure. Find the test statistic needed to test the claim.
Vegetarians
n1 = 85
Nonvegetarians
n2 = 75
x1 = 124.1 mmHg
s1 = 38.7 mmHg
A) -2.365
x2 = 138.7 mmHg
s2 = 39.2 mmHg
B) 0.0096
C) -2.589
D) 0.0057
10) Determine the slope of the least square regression line.
x
1
3
5 7 9
y 143 116 100 98 90
A) 140.4
B) -6.2
C) 150.7
3
D) 6.8
11) The table below shows the age and favorite type of music of 668 randomly selected
people. Determine the test statistic needed to test the claim that age and music preference
are independent.
Rock Pop Classical
15-25
50 85
73
25-35
68 91
60
35-45
90 74
77
A) 12.954
B) 16.919
C) 9.488
D) 11.143
12) You roll a die 48 times with the following results.
Number 1 2 3 4 5 6
Frequency 13 3 12 15 2 3
Find the test statistic to test the claim that the die is fair.
A) 14.13
B) 7.092
C) 8
D) 22
13) A marketing survey involves product recognition in New York and California. Of 558
New Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the
product. Construct a 99% confidence interval for the difference between the two
population proportions.
A) -0.0177 < p1 - p2 < 0.1243
C) -0.0443 < p1 - p2 < 0.0976
B) -0.0034 < p1 - p2 < 0.0566
D) 0.0247 < p1 - p2 < 0.0286
14) In studying the occurrence of genetic characteristics, the following sample data were
obtained. Find the critical value needed to test the claim that the characteristics occur with
the same frequency at the 0.05 significance level.
Characteristic A B C D E F
Frequency
28 30 45 48 38 39
A) 12.592
B) 8.263
C) 16.750
D) 11.071
^
15) Ten pairs of data yield the regression equation y = 2.08 + 3.29x. What is the predicted
value of y for x = 2?
A) 17.0
B) 8.66
C) 8.0
4
D) 7.0
16) Find the equation of the least squares regression line.
x 1.2 1.4 1.6 1.8 2.0
y 54 53 55 54 56
^
B) y = 50.4 + 2.50x
^
^
D) y = 54
A) y = 50 + 3x
^
C) y = 55.3 + 2.40x
17) From a sample of 5000 American Airlines passengers, 22 had their luggage lost. From a
sample of 4000 Delta Airlines passengers, 15 were lost. What is the test statistic for
testing the claim that the proportion of luggage lost is the same for both airlines
(H1: pAA pDA)?
A) 0.4037
B) 0.632
C) 0.5119
D) 0.4788
18) A researcher was interested in comparing the GPAs of students at two different colleges.
Independent simple random samples of 8 students from college A and 13 students from
college B yielded the following GPAs. Determine the alternative hypothesis to test the
claim that the mean GPA is higher for College B.
College A College B
3.7
3.8
3.2
3.2
3.0
3.0
2.5
3.9
2.7
3.8
3.6
2.5
2.8
3.9
3.4
A) H1: µA > µB
2.8
4.0
3.6
2.6
4.0
3.6
B) H1: µA < µB
C) H1: µA
µB
D) H1: µA
µB
19) It is claimed that the proportion of gloves that leak virus is greater for vinyl (V) gloves
than latex (L) gloves. What is H1 for testing this claim?
A) H1: pV
pL
B) H1: pV < pL
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C) H1: pV > pL
D) H1: pV
pL
20) A marketing survey involves product recognition in New York and California. Of 558
New Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the
product. At the 0.05 significance level, find the p-value to test the claim that the
recognition rates are the same in both states.
A) 0.333
B) 0.968
C) 0.459
D) 0.013
21) A paint manufacturer wished to compare the drying times of two different types of paint.
Independent simple random samples of 11 cans of type A and 9 cans of type B were
selected and applied to similar surfaces. The drying times, in hours, were recorded. The
summary statistics are as follows. Construct a 98% confidence interval for µ1 - µ2, the
difference between the mean drying time for paint of type A and the mean drying time
for paint of type B.
Type A
Type B
x1 = 77.5 hrs x2 = 63.6 hrs
s1 = 4.5 hrs s2 = 5.1 hrs
n1 = 11
n2 = 9
A) 8.35 hrs < µ1 - µ2 < 19.45 hrs
C) 8.42 hrs < µ1 - µ2 < 19.38 hrs
B) 8.58 hrs < µ1 - µ2 < 19.22 hrs
D) 8.28 hrs < µ1 - µ2 < 19.52 hrs
22) We wish to test a hypothesis about paired data. Suppose that d = 3.345, Sd = 1.984, and
n = 12, and that you wish to test H1: µd > 0. Determine the critical value needed to test
the hypothesis at the 0.01 level of significance.
A) 3.106
B) 2.718
C) 2.576
D) 2.326
\
23) A farmer has decided to use a new additive to grow his crops. He divided his farm into 10
plots and kept records of the corn yield (in bushels) before and after using the additive.
The results are shown below. What is the test statistic needed to test the claim that the
additive increases the yield?
Plot:
1
Before 9
After 10
A) -1.584
2
9
9
3
8
9
4
7
8
5
6
7
6
8
10
7
5
6
B) -2.033
8
9
10
9
10
10
C) -5.014
6
10
11
12
D) -2.536
24) If d = 3.125, Sd = 2.911, and n = 8, determine a 95 percent confidence interval for µd.
A) 2.264 < µd < 5.559
B) 0.691 < µd < 5.559
C) 0.691 < µd < 3.986
D) 2.264 < µd < 3.986
25) Suppose you wish to test the claim that µ d, the mean value of the differences d for a
population of paired data, is less than 0. Given a sample of n = 23 and a significance level
of = 0.05, what criterion would be used for rejecting the null hypothesis?
A) Reject H0 if the test statistic is less than -1.717.
B) Reject H0 if the test statistic is less than 1.717.
C) Reject H0 if the test statistic is less than -1.714.
D) Reject H0 if the test statistic is less than 1.714.
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