Download SHORT ANSWER. Write the word or phrase that best

Math 1342
Final Exam Review
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Construct and interpret a boxplot or a modified boxplot as specified.
1) The weights (in pounds) of 30 newborn babies are listed below. Construct a boxplot for the
data.
5.5 5.7 5.8 5.9 6.1 6.1 6.3 6.4 6.5 6.6
6.7 6.7 6.7 6.9 7.0 7.0 7.0 7.1 7.2 7.2
7.4 7.5 7.7 7.7 7.8 8.0 8.1 8.1 8.3 8.7
2) The test scores of 40 students are listed below. Construct a boxplot for the data.
25
59
73
81
35
62
73
82
43
63
74
83
44
65
76
85
47
66
77
89
48
68
77
92
54
69
78
93
55
69
79
94
56
71
80
97
1)
2)
57
71
81
98
Find the indicated probability or percentage for the normally distributed variable.
3) The incomes of trainees at a local mill are normally distributed with a mean of $1,100 and a
standard deviation $150. What percentage of trainees earn less than $900 a month?
3)
4) The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz
and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a
randomly selected bottle will be less than 32 oz?
4)
5) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a
mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the
probability of a rating that is between 200 and 275.
5)
6) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a
mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the
probability of a rating that is between 170 and 220.
6)
7) The lengths of human pregnancies are normally distributed with a mean of 268 days and a
standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300
days?
7)
8) Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a
standard deviation 0.070 g. A vending machine will only accept coins weighing between
5.48 g and 5.82 g. What percentage of legal quarters will be rejected?
8)
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Find the confidence interval specified.
9) Physiologists often use the forced vital capacity as a way to assess a person's ability to move
air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of
people suffering from asthma. A random sample of 15 asthmatics yields the following
data on forced vital capacity, in liters.
9)
3.0 4.8 5.3 4.6 3.6
3.7 3.7 4.3 3.5 5.2
3.2 3.5 4.8 4.0 5.1
Use the data to obtain a 95.44% confidence interval for the mean forced vital capacity for
all asthmatics. Assume that σ = 0.7.
10) A random sample of 106 light bulbs had a mean life of x = 526 hours. Assume that
σ = 29 hours. Construct a 90% confidence interval for the mean life, μ, of all light bulbs of
this type.
10)
11) A random sample of 131 full-grown lobsters had a mean weight of 20 ounces. Assume that
σ = 3.9 ounces. Construct a 95% confidence interval for the population mean μ.
11)
Find the confidence interval specified. Assume that the population is normally distributed.
12) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol
was 243 milligrams with s = 16.2 milligrams. Construct a 95% confidence interval for the
true mean cholesterol content of all such eggs.
12)
13) Thirty randomly selected students took the calculus final. If the sample mean was 83 and
the standard deviation was 14.1, construct a 99% confidence interval for the mean score of
all students.
13)
14) A sociologist develops a test to measure attitudes about public transportation, and 27
randomly selected subjects are given the test. Their mean score is 76.2 and their standard
deviation is 21.4. Construct the 95% confidence interval for the mean score of all such
subjects.
14)
Provide an appropriate response.
15) A hypothesis test is performed at the 5% significance level to determine whether the mean
body temperature for a certain population differs from 37.1° C. The hypotheses are
H : μ = 37.1° C
0
H : μ ≠ 37.1° C.
a
Explain the difference between statistical significance and practical significance.
16) A right-tailed hypothesis test for a population mean is to be performed. If the null
hypothesis is rejected at the 5% level of significance, does this necessarily mean that it
would be rejected at the 1% level of significance? at the 10% level of signifiance? Explain
your reasoning. In your explanation, refer to the critical values corresponding to the
different significance levels.
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15)
16)
17) In 1995, the mean math SAT score for students at one school was 488. A teacher introduces
a new teaching method to prepare students for the SAT. One year later, he performs a
hypothesis test to determine whether the mean math SAT score has increased. The
hypotheses are
H : μ = 488
0
H : μ > 488.
a
If the null hypothesis is rejected at the 10% level of significance, do you think the teacher
would feel confident that his teaching method works? What about if the null hypothesis is
rejected at the 1% level of significance? Which of these two results would constitute
stronger evidence that his teaching method works? Explain your thinking.
17)
Preliminary data analyses indicate that it is reasonable to use a t-test to carry out the specified hypothesis test. Perform
the t-test using the critical-value approach.
18) A test of sobriety involves measuring the subject's motor skills. The mean score for men
18)
who are sober is known to be 35.0. A researcher would like to perform a hypothesis test to
determine whether the mean score for sober women differs from 35.0. Twenty randomly
selected sober women take the test and produce a mean score of 41.0 with a standard
deviation of 3.7. Perform the hypothesis test at the 0.01 level of significance.
19) A large software company gives job applicants a test of programming ability and the mean
for that test has been 160 in the past. Twenty-five job applicants are randomly selected
from a large university and they produce a mean score of 183 and standard deviation of 12.
Use a 0.05 level of significance to test whether the mean score for students from this
university is greater than 160.
19)
20) In one state, the mean time served in prison by convicted burglars is 18.7 months. A
researcher would like to perform a hypothesis test to determine whether the mean amount
of time served by convicted burglars in her hometown is different from 18.7 months. She
takes a random sample of 11 such cases from court files in her home town and finds that
20)
x = 20.7 months and s = 7.7 months. Use a significance level of 0.05 to perform the test.
Apply the pooled t-interval procedure to obtain the required confidence interval. You may assume that the assumptions
for using the procedure are satisfied.
21) A researcher was interested in comparing the amount of time spent watching television by
21)
women and by men. Independent simple random samples of 14 women and 17 men were
selected and each person was asked how many hours he or she had watched television
during the previous week. The summary statistics are as follows.
Women
Men
x1 = 11.4 x2 = 17.4
s1 = 4.0 s2 = 4.1
n 1 = 14 n 2 = 17
Determine a 95% confidence interval for the difference between the mean weekly television
watching times of women and men.
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22) A paint manufacturer wanted 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.
Type A
22)
Type B
x1 = 70.0 x2 = 67.0
s1 = 3.6 s2 = 3.1
n 1 = 11
n2 = 9
Determine a 99% confidence interval for the difference between the mean drying time of
type A and the mean drying time of type B.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
23) The test scores of 40 students are summarized in the frequency distribution below. Find the
standard deviation.
Score Students
50 60
5
60 70
9
10
70 80
80 90
8
90 100
8
A) s = 11.9
B) s = 13.9
C) s = 13.2
D) s = 12.5
24) The manager of a bank recorded the amount of time each customer spent waiting in line during
peak business hours one Monday. The frequency distribution below summarizes the results. Find
the standard deviation. Round your answer to one decimal place.
Waiting time Number of
(minutes) customer
0 4
14
11
4 8
8 12
7
12 16
16
16 20
0
20 24
2
A) 5.6
B) 7.0
C) 5.3
4
23)
D) 5.9
24)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Preliminary data analyses indicates that use of a paired t-test is reasonable. Perform the hypothesis test by using either
the critical-value approach or the P-value approach as indicated.
25) Five students took a math test before and after tutoring. Their scores were as follows.
25)
Subject A B C D E
Before 70 73 76 80 77
After 74 82 74 83 89
At the 1% significance level, do the data provide sufficient evidence to conclude that the
mean score before tutoring differs from the mean score after tutoring? Use the
critical-value approach.
26) A coach uses a new technique in training middle distance runners. The times, in seconds,
for 8 different athletes to run 800 meters before and after this training are shown below.
26)
Athlete
A
B
C
D
E
F
G
H
Before 118.4 111.8 108.8 115.3 112.8 113.8 114.9 110.5
After 119 110.5 106.4 116.1 111 113.9 111.3 106.6
At the 5% significance level, do the data provide sufficient evidence that the training helps
to improve times for the 800 meters? Use the critical-value approach.
Use the paired t-interval procedure to obtain the required confidence interval. You may assume that the conditions for
using the procedure are satisfied.
27) Using the sample paired data below, determine a 90% confidence interval for the
27)
difference between the mean of x and the mean of y.
x 4.0 5.1 6.0 3.5 5.9
y 3.7 3.9 5.6 4.2 3.6
28) A coach uses a new technique in training middle distance runners. The times, in seconds,
for 9 different athletes to run 800 meters before and after this training are shown below.
28)
Athlete A
B
C
D
E
F
G
H
I
Before 115.2 120.9 108.0 112.4 107.5 119.1 121.3 110.8 122.3
After 116.0 119.1 105.1 111.9 109.1 115.2 118.5 110.7 120.9
Determine a 99% confidence interval for the difference between the mean time before and
after training.
Use the one-proportion z-interval procedure to find the required confidence interval.
29) A researcher wishes to estimate the proportion of adults in the city of Darby who are
vegetarian. In a random sample of 770 adults from this city, the proportion that are
vegetarian is 0.067. Find a 95% confidence interval for the proportion of all adults in the
city of Darby that are vegetarians.
30) In a sample of 713 patients who underwent a certain type of surgery, 22% experienced
complications. Find a 90% confidence interval for the proportion of all those undergoing
this surgery who experience complications.
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29)
30)
31) A survey of 300 union members in New York State reveals that 112 favor the Republican
candidate for governor. Construct the 98% confidence interval for the proportion of all
New York State union members who favor the Republican candidate.
31)
Use the one-proportion z-test to perform the required hypothesis test. Use the critical-value approach.
32) A manufacturer considers his production process to be out of control when defects exceed
32)
3%. In a random sample of 85 items, the defect rate is 5.9% but the manager claims that this
is only a sample fluctuation and that production is not really out of control. At the 0.01
level of significance, do the data provide sufficient evidence that the percentage of defects
exceeds 3%?
33) An airline's public relations department says that the airline rarely loses passengers'
luggage. It further claims that on those occasions when luggage is lost, 88% is recovered
and delivered to its owner within 24 hours. A consumer group who surveyed a large
number of air travelers found that only 133 out of 160 people who lost luggage on that
airline were reunited with the missing items by the next day. At the 5% level of
significance, do the data provide sufficient evidence to conclude that the proportion of
times that luggage is returned within 24 hours is less than 0.88?
33)
34) A poll of 1,068 adult Americans reveals that 48% of the voters surveyed prefer the
Democratic candidate for the presidency. At the 0.05 level of significance, do the data
provide sufficient evidence that the percentage of all voters who prefer the Democrat is
less than 50%?
34)
Use the two-proportions z-interval procedure to obtain the required confidence interval for the difference between two
population proportions. Assume that independent simple random samples have been selected from the two populations.
35) In a random sample of 43 Democrats from one city, 21 approved of the mayor's
35)
performance. In a random sample of 58 Republicans from the city, 34 approved of the
mayor's performance. Find a 90% confidence interval for the difference between the
proportions of Democrats and Republicans who approve of the mayor's performance.
36) A survey found that 37 of 76 randomly selected women and 43 of 77 randomly selected
men follow a regular exercise program. Find a 95% confidence interval for the difference
between the proportions of women and men who follow a regular exercise program.
36)
Use the regression equation to predict the y-value corresponding to the given x-value. Round your answer to the nearest
tenth.
37) The regression equation relating dexterity scores (x) and productivity scores (y) for ten
37)
^
randomly selected employees of a company is y = 5.50 + 1.91x. Predict the productivity
score for an employee whose dexterity score is 32.
38) The regression equation relating attitude rating (x) and job performance rating (y) for ten
^
randomly selected employees of a company is y = 11.7 + 1.02x. Predict the job performance
rating for an employee whose attitude rating is 67.
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38)
Answer Key
Testname: FINAL EXAM REVIEW
1)
The data is highly symmetrical. It is a uniform distribution.
2)
The data is slightly left-skewed.
3) 9.18%
4) 0.4013
5) 0.4332
6) 0.3811
7) 0.0166
8) 1.96%
9) 3.79 to 4.51 liters
10) 521.4 to 530.6 hours
11) 19.3 to 20.7 ounces
12) 232.7 to 253.3 milligrams
13) 75.91 to 90.09
14) 67.7 to 84.7
15) Answers will vary. Possible answer: The results are statistically significant at the 5% significance level if the null
hypothesis is rejected. This means that the data provide evidence to conclude that μ ≠ 37.1° C. However, even if the
results are statistically significant, this does not necessarily imply practical significance - the difference between μ and
37.1° C could be too small to be of practical importance.
16) A null hypothesis which is rejected at the 5% level of significance will certainly be rejected at the 10% level of
significance but not necessarily at the 1% level of significance. If the null hypothesis is rejected at the 5% level of
significance, the test statistic is greater than the critical value of 1.645. This means that the test statistic is certainly
greater than 1.28 which is the critical value corresponding to a 10% level of significance. The test statistic is not
necessarily greater than 2.33 which is the critical value corresponding to a 1% level of significance.
17) If the null hypothesis is rejected at the 1% level of significance this provides much stronger evidence that μ > 488 than
if the null hypothesis is rejected at the 10% level of significance. Suppose that his teaching method actually does not
work and that μ = 488. Then the chance that the null hypothesis would be rejected at the 10% level is 10%. This is not
so unlikely. However, the chance that the null hypothesis would be rejected at the 1% level is only 1%.
18) H : μ = 35.0. H : μ ≠ 35.0.
0
a
α = 0.01
Test statistic: t = 7.252. Critical values: t = -2.861, 2.861. Reject the null hypothesis. At the 1% level of significance, there
is sufficient evidence to conclude that the mean score for sober women differs from 35.0, the mean score for men.
19) H : μ = 160. H : μ > 160.
0
a
α = 0.05
Test statistic: t = 9.583. Critical value: t = 1.711. Reject the null hypothesis. At the 5% level of significance, there is
sufficient evidence to conclude that the mean score for students from this university is greater than 160.
7
Answer Key
Testname: FINAL EXAM REVIEW
20) H
: μ = 18.7 months. H : μ ≠ 18.7 months.
0
a
α = 0.05
Test statistic: t = 0.86. Critical values: t = ±2.228. Do not reject H
. At the 5% level of significance, there is not sufficient
0
evidence to conclude that the mean amount of time served by convicted burglars in her hometown is different from
18.7 months.
21) -8.99 to -3.01 hours
22) -1.38 to 7.38 hours
23) C
24) A
25) H0 : μ1 = μ2
Ha : μ1 ≠ μ2
α = 0.01
t = -2.134
Critical values = ±4.604
Do not reject H0 . At the 1% significance level, the data do not provide sufficient evidence to conclude that the mean
score before tutoring differs from the mean score after tutoring.
26) H0 : μ1 = μ2
Ha : μ1 > μ2
α = 0.05
t = 2.227
Critical value = 1.895
Reject H0 . At the 5% significance level, the data provide sufficient evidence to conclude that the training helps to
improve times for the 800 meters.
27) -0.37 to 1.77
28) -0.82 to 3.26 seconds
29) 0.0493 to 0.0847
30) 0.1945 to 0.2455
31) 0.308 to 0.438
32) H0 : p = 0.03 Ha : p > 0.03.
α = 0.01
Test statistic: z = 1.57. Critical value: z = 2.33.
Do not reject the null hypothesis. At the 1% significance level, the data do not provide sufficient evidence to conclude
that the percentage of defects exceeds 3%.
33) H0 : p = 0.88; Ha : p < 0.88;
α = 0.05
Test statistic: z = -1.90. Critical value = -1.645
Reject H0 . At the 5% level of significance, the data provide sufficient evidence to conclude that the proportion of times
that luggage is returned within 24 hours is less than 0.88
34) H0 : p = 0.5 Ha : p < 0.5.
α = 0.05
Test statistic: z = -1.31. Critical value: z = -1.645.
Do not reject the null hypothesis. At the 5% level of significance, the data do not provide sufficient evidence to
conclude that the percentage of voters who prefer the Democrat is less than 50%.
35) -0.262 to 0.067
36) -0.229 to 0.086
37) 66.6
38) 80.0
8