MATH 1342 TEST ON CHAPTER 10
ANSWER ALL QUESTIONS. TIME 1.5 HOURS
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1) A researcher wants to determine whether the number of minutes adults spend online per day is
related to gender. A random sample of 315 adults was selected and the results are shown below.
1)
2
Find the critical value χ 0 to determine if there is enough evidence to conclude that the number of
minutes spent online per day is related to gender. Use α = 0.05.
Minutes spent online per day
Gender 0-30 30-60 60-90 90+
Male
25 35 75
45
Female 30 45 45
15
A) 9.348
B) 11.345
C) 6.251
D) 7.815
Find the indicated expected frequency.
2) A researcher wants to determine whether the number of minutes adults spend online per day is
related to gender. A random sample of 315 adults was selected and the results are shown below.
Find the expected frequency for the cell E2,2 to determine if there is enough evidence to conclude
2)
that the number of minutes spent online per day is related to gender. Round to the nearest tenth if
necessary.
Minutes spent online per day
Gender 0-30 30-60 60-90 90+
Male
22
34
74
50
Female
30
42
42
21
A) 49.7
B) 32.6
C) 43.4
D) 66.3
Provide an appropriate response.
3) A sports researcher is interested in determining if there is a relationship between the number of
home team and visiting team wins and different sports. A random sample of 526 games is selected
2
and the results are given below. Find the critical value χ 0 to test the claim that the number of
home team and visiting team wins is independent of the sport. Use α = 0.01.
Football Basketball Soccer Baseball
Home team wins 39
156
25
83
Visiting team wins 31
98
19
75
A) 9.348
B) 11.345
C) 7.815
1
D) 12.838
3)
Find the indicated expected frequency.
4) The contingency table below shows the results of a random sample of 400 state representatives that
was conducted to see whether their opinions on a bill are related to their party affiliation.
4)
Opinion
Party
Approve Disapprove No Opinion
Republican
84
40
28
Democrat
100
48
36
Independent
20
32
12
Find the expected frequency for the cell E2,2. Round to the nearest tenth if necessary.
A) 93.84
B) 45.6
C) 55.2
D) 34.96
Provide an appropriate response.
5) A sports researcher is interested in determining if there is a relationship between the type of sport
and type of team winning (home team versus visiting team). A random sample of 526 games is
selected and the results are given below. Calculate the chi-square test statistic χ 2 to test the claim
5)
that the type of team winning is independent of the sport.
Football Basketball Soccer Baseball
Home team wins 39
156
25
83
Visiting team wins 31
98
19
75
A) 2.919
B) 4.192
C) 3.290
D) 5.391
Find the indicated expected frequency.
6) A medical researcher is interested in determining if there is a relationship between adults over 50
who walk regularly and low, moderate, and high blood pressure. A random sample of 236 adults
over 50 is selected and the results are given below. Find the expected frequency E2,2 to test the
6)
claim that walking and low, moderate, and high blood pressure are not related. Round to the
nearest tenth if necessary.
Blood Pressure Low Moderate High
Walkers
32
68
22
Non-walkers
24
69
21
A) 66.2
B) 70.8
C) 27.1
D) 20.8
Provide an appropriate response.
7) The contingency table below shows the results of a random sample of 200 state representatives that
was conducted to see whether their opinions on a bill are related to their party affiliation. Opinion
Party
Approve Disapprove No Opinion
Republican
42
20
14
Democrat
50
24
18
Independent
10
16
6
2
Find the critical value χ 0 , to test the claim of independence using α = 0.05.
A) 9.488
B) 7.779
C) 13.277
2
D) 11.143
7)
Find the marginal frequencies for the given contingency table.
8)
Blood Type
O A B AB
Sex
F
104 92 18 11
M 75 68 15 7
A)
8)
B)
104
92
18
11
225
104
92
18
11
235
75
68
15
7
165
75
68
15
7
165
179
160
33
18
390
179
160
33
18
400
C)
D)
104
92
18
11
225
104
92
18
11
215
75
68
15
7
160
75
68
15
7
175
179
160
33
18
390
179
160
33
17
390
Provide an appropriate response.
9) A researcher wants to determine whether the number of minutes adults spend online per day is
related to gender. A random sample of 315 adults was selected and the results are shown below.
Calculate the chi-square test statistic χ 2 to determine if there is enough evidence to conclude that
the number of minutes spent online per day is related to gender.
Minutes spent online per day
Gender 0-30 30-60 60-90 90+
Male
25 35 75
45
Female 30 45 45
15
A) 21.231
B) 18.146
C) 19.874
3
D) 20.912
9)
10) A random sample of 160 car crashes are selected and categorized by age. The results are listed
below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39%
for the 26-45 group, 31% for the 45-65 group, and 12% for the group over 65. Find the critical
10)
2
value χ 0 to test the claim that all ages have crash rates proportional to their driving rates.
Use α = 0.05.
Age
Under 26 26 - 45 46 - 65 Over 65
Drivers
66
39 25 30
A) 7.815
B) 11.143
C) 9.348
D) 6.251
11) A random sample of 160 car crashes are selected and categorized by age. The results are listed
below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39%
for the 26-45 group, 31% for the 45-65 group, and 12% for the group over 65. Calculate the
chi-square test statistic χ 2 to test the claim that all ages have crash rates proportional to their
11)
driving rates.
Age
Under 26 26 - 45 46 - 65 Over 65
Drivers
66
39 25 30
A) 85.123
B) 95.431
C) 75.101
D) 101.324
1
12) Each side of a standard six-sided die should appear approximately of the time when the die is
6
12)
rolled. A player suspects that a certain die is loaded. The suspected die is rolled 90 times. The
results are shown below. Calculate the chi-square test statistic χ 2 to test the playerʹs claim.
Number 1 2 3 4 5 6
Frequency 15 19 16 11 17 12
A) 5.013
B) 3.067
C) 4.312
D) 2.143
1
13) Each side of a standard six-sided die should appear approximately of the time when the die is
6
13)
rolled. A player suspects that a certain die is loaded. The suspected die is rolled 90 times. The
2
results are shown below. Find the critical value χ 0 to test the playerʹs claim. Use α = 0.10.
Number 1 2 3 4 5 6
Frequency 17 19 12 16 15 11
A) 1.610
B) 12.833
C) 9.236
D) 11.071
14) A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee.
A sample of 200 customers provided the data below. Calculate the chi-square test statistic χ 2 to
test the claim that the distribution is uniform..
Brand
1 2 3 4 5
Customers 55 30 18 65 32
A) 55.63
B) 48.91
C) 45.91
4
D) 37.45
14)
15) A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee.
15)
2
A sample of 200 customers provided the data below. Find the critical value χ 0 to test the claim
that the distribution is uniform. Use α = 0.01.
Brand
1 2 3 4 5
Customers 32 55 30 65 18
A) 13.277
B) 14.860
C) 9.488
D) 11.143
16) A teacher figures that final grades in the statistics department are distributed as: A, 25%; B, 25%; C,
40%; D, 5%; F, 5%. At the end of a randomly selected semester, the following number of grades
were recorded. Calculate the chi-square test statistic χ 2 to determine if the grade distribution for
16)
the department is different than expected.
Grade A B C D F
Number 42 36 60 8 14
A) 3.41
B) 4.82
C) 6.87
D) 5.25
17) Many track runners believe that they have a better chance of winning if they start in the inside lane
that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is
Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track
runners in the different starting positions. Calculate the chi-square test statistic χ 2 to test the claim
17)
that the number of wins is uniformly distributed across the different starting positions. The results
are based on 240 wins.
Starting Position 1 2 3 4 5 6
Number of Wins 36 45 44 33 50 32
A) 15.541
B) 9.326
C) 6.750
D) 12.592
18) A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee.
A sample of 200 customers provided the data below. Calculate the chi-square test statistic χ 2 to
18)
test the claim that the distribution is uniform..
Brand
1 2 3 4 5
Customers 30 55 32 65 18
A) 48.91
B) 45.91
C) 55.63
D) 37.45
19) A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee.
2
A sample of 200 customers provided the data below. Find the critical value χ 0 to test the claim
that the distribution is uniform. Use α = 0.01.
Brand
1 2 3 4 5
Customers 65 55 30 32 18
A) 13.277
B) 11.143
C) 9.488
5
D) 14.860
19)
20) The contingency table below shows the results of a random sample of 200 state representatives that
was conducted to see whether their opinions on a bill are related to their party affiliation.
Opinion
Party
Approve Disapprove No Opinion
Republican
42
20
14
Democrat
50
24
18
Independent
10
16
6
Find the chi-square test statistic, χ 2 , to test the claim of independence.
A) 11.765
B) 7.662
C) 9.483
6
D) 8.030
20)
Answer Key
Testname: M1342C10A
1) D
2) B
3) B
4) C
5) C
6) A
7) A
8) A
9) B
10) A
11) C
12) B
13) C
14) D
15) A
16) D
17) C
18) D
19) A
20) D
7