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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
1) The dean of a major university claims that the mean time for students to earn a Masterʹs
degree is at most 4.9 years. Write the null and alternative hypotheses.
1)
2) The mean score for all NBA games during a particular season was less than 101 points per
game. State this claim mathematically. Write the null and alternative hypotheses. Identify
which hypothesis is the claim.
2)
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3) Given H0 : p ≥ 80% and Ha : p < 80%, determine whether the hypothesis test is left-tailed,
3)
right-tailed, or two-tailed.
A) right-tailed
B) left-tailed
C) two-tailed
4) A researcher claims that 62% of voters favor gun control. Determine whether the hypothesis test
for this claim is left-tailed, right-tailed, or two-tailed.
A) left-tailed
B) two-tailed
4)
C) right-tailed
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
5) The mean age of bus drivers in Chicago is 52.5 years. Identify the type I and type II errors
for the hypothesis test of this claim.
5)
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6) The mean age of bus drivers in Chicago is 59.3 years. If a hypothesis test is performed, how should
you interpret a decision that fails to reject the null hypothesis?
6)
A) There is sufficient evidence to support the claim μ = 59.3.
B) There is sufficient evidence to reject the claim μ = 59.3.
C) There is not sufficient evidence to support the claim μ = 59.3.
D) There is not sufficient evidence to reject the claim μ = 59.3.
7) The mean IQ of statistics teachers is greater than 160. If a hypothesis test is performed, how should
you interpret a decision that rejects the null hypothesis?
A) There is not sufficient evidence to reject the claim μ > 160.
B) There is sufficient evidence to reject the claim μ > 160.
C) There is sufficient evidence to support the claim μ > 160.
D) There is not sufficient evidence to support the claim μ > 160.
1
7)
8) Given H0 : μ ≤ 12, for which confidence interval should you reject H0 ?
A) (11.5, 12.5)
B) (10, 13)
8)
C) (13, 16)
9) Suppose you are using α = 0.05 to test the claim that μ > 14 using a P-value. You are given the
9)
sample statistics n = 50, x = 14.3, and s = 1.2. Find the P-value.
A) 0.0128
B) 0.0384
C) 0.1321
D) 0.0012
10) Given H0 : μ ≥ 18 and P = 0.070. Do you reject or fail to reject H0 at the 0.05 level of significance?
10)
A) not sufficient information to decide
B) reject H0
C) fail to reject H0
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
11) A fast food outlet claims that the mean waiting time in line is less than 3.4 minutes. A
random sample of 60 customers has a mean of 3.3 minutes with a standard deviation of 0.6
minute. If α = 0.05, test the fast food outletʹs claim.
11)
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12) You wish to test the claim that μ > 32 at a level of significance of α = 0.05 and are given sample
12)
statistics n = 50, x = 32.3, and s = 1.2. Compute the value of the standardized test statistic. Round
your answer to two decimal places.
A) 1.77
B) 3.11
C) 0.98
D) 2.31
13) Suppose you want to test the claim that μ ≥ 65.4. Given a sample size of n = 35 and a level of
significance of α = 0.05, when should you reject H0 ?
13)
A) Reject H0 if the standardized test statistic is less than -1.28.
B) Reject H0 if the standardized test statistic is less than -2.575.
C) Reject H0 if the standardized test is less than -1.96.
D) Reject H0 if the standardized test statistic is less than -1.645.
14) Find the standardized test statistic t for a sample with n = 12, x = 22.2, s = 2.2, and α = 0.01 if
H0 : μ = 21. Round your answer to three decimal places.
A) 2.001
B) 1.890
C) 2.132
2
D) 1.991
14)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
15) A local group claims that the police issue more than 60 speeding tickets a day in their area.
To prove their point, they randomly select two weeks. Their research yields the number of
tickets issued for each day. The data are listed below. At α = 0.01, test the groupʹs claim
using P-values.
15)
70 48 41 68 69 55 70
57 60 83 32 60 72 58
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16) Determine whether the normal sampling distribution can be used. The claim is p < 0.25 and the
sample size is n = 18.
A) Use the normal distribution.
16)
B) Do not use the normal distribution.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
17) An airline claims that the no-show rate for passengers is less than 5%. In a sample of 420
randomly selected reservations, 19 were no-shows. At α = 0.01, test the airlineʹs claim.
17)
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18) Compute the standardized test statistic, X2 , to test the claim σ2 = 21.5 if n = 12, s2 = 18, and
α = 0.05.
A) 9.209
B) 18.490
C) 12.961
18)
D) 0.492
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
19) A trucking firm suspects that the variance for a certain tire is greater than 1,000,000. To
check the claim, the firm puts 101 of these tires on its trucks and gets a standard deviation
of 1200 miles. If α = 0.05, test the trucking firmʹs claim using P-values.
19)
Identify the explanatory variable and the response variable.
20) An agricultural business wants to determine if the rainfall in inches can be used to predict
the yield per acre on a wheat farm.
20)
Provide an appropriate response.
21) The data below are the gestation periods, in months, of randomly selected animals and
their corresponding life spans, in years. Construct a scatter plot for the data. Determine
whether there is a positive linear correlation, a negative linear correlation, or no linear
correlation.
Gestation, x
Life span, y
8
30
2.1
12
1.3
6
1
3
11.5
25
5.3
12
3
3.8
10
24.3
40
21)
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22) The data below are the number of absences and the final grades of 9 randomly selected students
from a statistics class. Calculate the correlation coefficient, r.
Number of absences, x
Final Grade, y
A) -0.918
22)
1 4 7 5 10 3 16 9 6
97 85 79 81 70 91 54 75 81
B) -0.899
C) -0.991
D) -0.888
23) Given a sample with r = -0.765, n = 22, and α = 0.02, determine the critical values t0 necessary to
23)
test the claim ρ = 0.
A) ± 2.528
B) ± 2.831
C) ± 1.721
D) ± 2.080
24)
24) Find the equation of the regression line for the given data.
x
y
-5 -3 4 1 -1 -2 0 2 3 -4
11 -6 8 -3 -2 1 5 -5 6 7
^
^
A) y = -2.097x + 0.206
B) y = 0.206x - 2.097
^
^
C) y = 2.097x - 0.206
D) y = -0.206x + 2.097
25) Use the regression equation to predict the value of y for x = -1.5. Assume that the variables x and y
have a significant correlation.
x
y
-5 -3 4 1 -1 -2 0 2 3 -4
11 6 -6 -1 3 4 1 -4 -5 8
A) -2.069
B) -3.022
C) 3.586
D) 0.748
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
26) Find the equation of the regression line by letting Row 1 represent the x-values and Row 2
represent the y-values. Now find the equation of the regression line letting Row 2
represent the x-values and Row 1 represent the y-values. What effect does switching the
explanatory and response variables have on the regression line?
Row 1 -5 -3 4 1 -1 -2 0 2 3 -4
Row 2 -10 -8 9 1 -2 -6 -1 3 6 -8
4
26)
25)
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^
27) Find the standard error of estimate, se, for the data below, given that y = -2.5x.
27)
x -1 -2 -3 -4
6
7
10
y 2
A) 0.675
B) 0.349
C) 0.532
D) 0.866
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
28) Calculate the coefficient of determination, given that the linear correlation coefficient, r, is
-0.625. What does this tell you about the explained variation and the unexplained
variation of the data about the regression line?
28)
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^
29) Construct a 95% prediction interval for y given x = 2.5, y = -2.5x and se = 0.866. Round interval to
29)
three decimal places.
x
y
-1 -2 -3 -4
2 6 7 10
A) -16.156 < y < 3.656
B) -15.566 < y < 3.066
C) -8.244 < y < -4.256
D) -12.594 < y < 0.094
^
30) A multiple regression equation is y = -35,000 + 130x1 + 20,000x2 , where x1 is a personʹs age, x2 is
the personʹs grade point average in college, and y is the personʹs income. Predict the income for a
person who is 34 years old and had a college grade point average of 2.5.
A) $19,420
B) $645,325
C) $54,420
D) $89,420
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
31) The frequency distribution shows the ages for a sample of 100 employees. Find the
expected frequencies for each class to determine if the employee ages are normally
distributed.
Class boundaries
29.5-39.5
39.5-49.5
49.5-59.5
59.5-69.5
69.5-79.5
Frequency, f
14
29
31
18
8
5
31)
30)
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32) 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
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) 12.592
B) 9.326
C) 15.541
D) 6.750
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
33) The frequency distribution shows the ages for a sample of 100 employees. Are the ages of
employees normally distributed? Use α = 0.05.
Class boundaries
29.5-39.5
39.5-49.5
49.5-59.5
59.5-69.5
69.5-79.5
Frequency, f
14
29
31
18
8
6
33)
32)
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Find the marginal frequencies for the given contingency table.
34)
34)
Blood Type
O A B AB
Sex
F
104 92 18 11
M 75 68 15 7
A)
B)
104
92
18
11
215
104
92
18
11
225
75
68
15
7
175
75
68
15
7
160
179
160
33
17
390
179
160
33
18
390
D)
C)
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
Provide an appropriate response.
35) 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) 7.662
B) 11.765
C) 8.030
7
D) 9.483
35)
2
2
36) Calculate the test statistic F to test the claim that σ 1 = σ 2 . Two samples are randomly selected
36)
from populations that are normal. The sample statistics are given below.
n 1 = 13
n 2 = 12
2
s 1 = 30.576
2
s 2 = 24.375
A) 1.254
B) 0.797
C) 1.573
D) 1.120
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
37) Find the left-tailed and right tailed critical F-values for a two-tailed test. Use the sample
statistics below. Let α = 0.05.
n 1 = 5
n 2 = 6
2
s 1 = 5.8
2
s 2 = 2.7
38) The weights of a random sample of 25 women between the ages of 25 and 34 had a
standard deviation of 28 pounds. The weights of a random sample of 41 women between
the ages of 55 and 64 had a standard deviation of 21 pounds. Construct a 95% confidence
σ1 2
, where σ1 2 and σ2 2 are the variances of the weights of women between
interval for σ2 2
37)
38)
the ages 25 and 34 and the weights of women between the ages of 55 and 64 respectively.
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39) Find the test statistic F to test the claim that the populations have the same mean.
Brand 1
n = 8
Brand 2
n = 8
Brand 3
n = 8
x = 3.0
s = 0.50
x = 2.6
s = 0.60
x = 2.6
s = 0.55
A) 1.182
B) 1.021
C) 1.403
8
D) 0.832
39)
40) A researcher wishes to determine whether there is a difference in the average age of elementary
school, high school, and community college teachers. Teachers are randomly selected. Their ages
are recorded below. Find the critical value F0 to test the claim that there is no difference in the
average age of each group. Use α = 0.01.
Elementary Teachers High School Teachers Community College Teachers
23
41
45
28
38
45
27
36
36
25
47
61
52
42
39
37
31
35
A) 5.42
B) 9.43
C) 6.36
9
D) 5.09
40)
Answer Key
Testname: 1342TEST4 REVIEW
1) H0 : μ ≤ 4.9, Ha : μ > 4.9
2) claim: μ < 101; H0 : μ ≥ 101, Ha : μ < 101; claim is Ha
3) B
4) B
5) type I: rejecting H0 : μ = 52.5 when μ = 52.5
type II: failing to reject H0 : μ = 52.5 when μ ≠ 52.5
6) D
7) C
8) C
9) B
10) C
11) Fail to reject H0 ; There is not enough evidence to support the fast food outletʹs claim that the mean waiting time is less
than 3.4 minutes.
12) A
13) D
14) B
15) P-value = 0.4766. Since the P-value is great than α, there is not sufficient evidence to support the the groupʹs claim.
16) B
17) critical value z 0 = -2.33; standardized test statistic ≈ -0.45; fail to reject H0 ; There is not sufficient evidence to support
the airlineʹs claim.
18) A
19) Standardized test statistic ≈ 144; Therefore, at a degree of freedom of 100, P must be less than 0.005. P < α, reject H0 ;
There is sufficient evidence to support the firmʹs claim.
20) explanatory variable: rainfall in inches; response variable: yield per acre
21)
There appears to be a positive linear correlation.
22) C
23) A
24) D
25) C
26) The sign of m is unchanged, but the values of m and b change.
27) D
28) The coefficient of determination, r2 , = 0.391. That is, 39.1% of the variation is explained and 60.9% of the variation is
unexplained.
29) B
10
Answer Key
Testname: 1342TEST4 REVIEW
30) A
31) 11, 26, 32, 21, and 7, respectively.
32) D
33) Critical value χ 0 2 = 9.488; chi-square test statistic χ 2 = 1.77; fail to reject H0 ; The ages of employees are normally
distributed.
34) C
35) C
36) A
37) FL = 0.107, FR = 7.39
38) (0.827, 3.573)
39) C
40) C
11