MAT1140 Final Exam Review
Provide an appropriate response.
1) The frequency distribution below summarizes employee years of service for Alpha Corporation. Determine the
width of each class.
Years of service Frequency
1-5
5
6-10
20
11-15
25
16-20
10
21-25
5
26-30
3
2) The frequency distribution below summarizes the home sale prices in the city of Summerhill for the month of
June. Determine the width of each class.
(Sale price in thousand $) Frequency
80.0 - 110.9
2
111.0 - 141.9
5
142.0 - 172.9
7
173.0 - 203.9
10
204.0 - 234.9
3
235.0 - 265.9
1
Provide an appropriate answer.
3) Use the following frequency distribution to determine the class limits of the next class if an additional class were
to be added.
Class Frequency
8-12
8
13-17
6
18-22
8
23-27
10
28-32
9
33-37
10
1
Provide an appropriate response.
4) In a survey, 26 voters were asked their ages. The results are shown below. Construct a histogram to represent
the data (with 5 classes beginning with a lower class limit of 19.5 and a class width of 10). What is the
approximate age at the center?
43 56 28 63 67 66 52 48 37 51 40 60 62
66 45 21 35 49 32 53 61 53 69 31 48 59
Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results.
5) When investigating times required for drive-through service, the following results (in seconds) were obtained.
Restaurant A 120 67 89 97 124 68 72 96
Restaurant B 115 126 49 56 98 76 78 95
Find the mean and median for each of the two samples, then compare the two sets of results.
6) The Body Mass Index (BMI) is measured for a random sample of men from two different colleges. Interpret the
results by determining whether there is a difference between the two data sets that is not apparent from a
comparison of the measures of center. If there is, what is it?
Baxter College 24 23.5 22 27 25 21.5 25 24
Banter College 19 20 24 25 31 18 29 28
Solve the problem. Round results to the nearest hundredth.
7) The mean of a set of data is 239.89 and its standard deviation is 63.56. Find the z score for a value of 475.68.
Find the number of standard deviations from the mean. Round your answer to two decimal places.
8) Mario's weekly poker winnings have a mean of $343 and a standard deviation of $61. Last week he won $180.
How many standard deviations from the mean is that?
2
Determine which score corresponds to the higher relative position.
9) Which score has a higher relative position, a score of 296.4 on a test for which x = 260 and s = 26, or a score of
45.2 on a test for which x = 40 and s = 4?
Find the indicated measure.
10) Use the given sample data to find Q3 .
49 52 52 52 74 67 55 55
Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots.
11) The weekly salaries (in dollars) of 24 randomly selected employees of a company are shown below. Construct a
boxplot for the data set.
310 320 450 460 470 500 520 540
580 600 650 700 710 840 870 900
1000 1200 1250 1300 1400 1720 2500 3700
Construct a modified boxplot for the data. Identify any outliers.
12) The weights (in ounces) of 27 tomatoes are listed below.
1.7 2.0 2.2 2.2 2.4 2.5 2.5 2.5 2.6
2.6 2.6 2.7 2.7 2.7 2.8 2.8 2.8 2.9
2.9 2.9 3.0 3.0 3.1 3.1 3.3 3.6 4.2
Determine which score corresponds to the higher relative position.
13) Which score has a higher relative position, a score of 82 on a test for which x = 67 and s = 10, or a score of 299.5
on a test for which x = 226 and s = 49?
A) Both scores have the same relative position.
B) A score of 299.5
C) A score of 82
Solve the problem. Round results to the nearest hundredth.
14) The mean height of a basketball team is 6.3 feet with a standard deviation of 0.2 feet. The team's center is 6.7 feet
tall. Find the center's z score. Is his score unusual?
A) 2.2, yes
B) 2, yes
C) 1.5, no
D) 1.7, no
3
15) A department store, on average, has daily sales of $28,072.79. The standard deviation of sales is $2000. On
Tuesday, the store sold $35,648.28 worth of goods. Find Tuesday's z score. Was Tuesday an unusually good
day?
A) 3.79, yes
B) 4.10, yes
C) 3.98, no
D) 3.03, no
Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied.
16)
x P(x)
1 0.037
2 0.200
3 0.444
4 0.296
17) If a person is randomly selected from a certain town, the probability distribution for the number, x, of siblings is
as described in the accompanying table.
x P(x)
0 0.28
1 0.26
2 0.20
3 0.11
4 0.08
5 0.02
Find the mean of the given probability distribution.
18) The random variable x is the number of houses sold by a realtor in a single month at the Sendsom's Real Estate
office. Its probability distribution is as follows.
Houses Sold (x) Probability P(x)
0
0.24
1
0.01
2
0.12
3
0.16
4
0.01
5
0.14
6
0.11
7
0.21
4
Provide an appropriate response. Round to the nearest hundredth.
19) Find the standard deviation for the given probability distribution.
x P(x)
0 0.07
1 0.14
2 0.34
3 0.18
4 0.27
Provide an appropriate response.
20) In a game, you have a 1/44 probability of winning $97 and a 43/44 probability of losing $7. What is your
expected value?
21) A 28-year-old man pays $64 for a one-year life insurance policy with coverage of $120,000. If the probability
that he will live through the year is 0.9994, what is the expected value for the insurance policy?
22) A contractor is considering a sale that promises a profit of $40,000 with a probability of 0.7 or a loss (due to bad
weather, strikes, and such) of $19,000 with a probability of 0.3. What is the expected profit?
Find the mean of the given probability distribution.
23) The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.4096, 0.4096,
0.1536, 0.0256, and 0.0016, respectively. Round answer to the nearest hundredth.
Find the indicated probability. Round to three decimal places.
24) A test consists of 10 true/false questions. To pass the test a student must answer at least 9 questions correctly. If
a student guesses on each question, what is the probability that the student will pass the test?
25) A machine has 7 identical components which function independently. The probability that a component will
fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the
machine will be working.
5
26) A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly
select and test 23 components and accept the whole batch if there are fewer than 3 defectives. If a particular
shipment of thousands of components actually has a 3% rate of defects, what is the probability that this whole
shipment will be accepted?
27) In a study, 42% of adults questioned reported that their health was excellent. A researcher wishes to study the
health of people living close to a nuclear power plant. Among 13 adults randomly selected from this area, only 3
reported that their health was excellent. Find the probability that when 13 adults are randomly selected, 3 or
fewer are in excellent health.
Find the indicated probability.
28) The brand name of a certain chain of coffee shops has a 58% recognition rate in the town of Coffleton. An
executive from the company wants to verify the recognition rate as the company is interested in opening a
coffee shop in the town. He selects a random sample of 10 Coffleton residents. Find the probability that exactly
4 of the 10 Coffleton residents recognize the brand name.
29) A multiple choice test has 7 questions each of which has 5 possible answers, only one of which is correct. If
Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer
exactly 3 questions correctly?
Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard
deviation 1.
30)
6
31)
32)
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
33) Shaded area is 0.4013.
34) Shaded area is 0.4483.
7
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C at
the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some
give readings below 0°C (denoted by negative numbers) and some give readings above 0°C (denoted by positive
numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°C. Also assume that the
frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and
tested. Find the temperature reading corresponding to the given information.
35) Find Q3 , the third quartile.
36) If 6.3% of the thermometers are rejected because they have readings that are too high and another 6.3% are
rejected because they have readings that are too low, find the two readings that are cutoff values separating the
rejected thermometers from the others.
Solve the problem.
37) The scores on a certain test are normally distributed with a mean score of 58 and a standard deviation of 2.
What is the probability that a sample of 90 students will have a mean score of at least 58.2108?
38) Suppose that replacement times for washing machines are normally distributed with a mean of 9.3 years and a
standard deviation of 1.1 years. Find the probability that 70 randomly selected washing machines will have a
mean replacement time less than 9.1 years.
39) 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 40 different applicants are randomly selected, find the probability that their mean is
above 215.
Find the indicated critical z value.
40) Find the value of -z /2 that corresponds to a confidence level of 92.50%.
41) Find the critical value z /2 that corresponds to a 91% confidence level.
8
Solve the problem.
42) The following confidence interval is obtained for a population proportion, p: (0.736, 0.774). Use these confidence
interval limits to find the margin of error, E.
43) The following confidence interval is obtained for a population proportion, p: 0.335 < p < 0.361. Use these
^
confidence interval limits to find the point estimate, p.
Solve the problem. Round the point estimate to the nearest thousandth.
44) 37 randomly picked people were asked if they rented or owned their own home, 18 said they rented. Obtain a
point estimate of the proportion of home owners.
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
45) Of 328 randomly selected medical students, 25 said that they planned to work in a rural community. Find a 95%
confidence interval for the true proportion of all medical students who plan to work in a rural community.
46) Of 121 randomly selected adults, 35 were found to have high blood pressure. Construct a 95% confidence
interval for the true percentage of all adults that have high blood pressure.
Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume
that the population has a normal distribution.
47) n = 10, x = 9.9, s = 4.5, 95% confidence
48) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 234 milligrams
with s = 12.7 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such
eggs.
9
Solve the problem.
49) Find the critical value
2
R corresponding to a sample size of 8 and a confidence level of 98 percent.
50) Find the chi-square value
2
L corresponding to a sample size of 10 and a confidence level of 99 percent.
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation .
Assume that the population has a normal distribution. Round the confidence interval limits to the same number of
decimal places as the sample standard deviation.
51) Weights of eggs: 95% confidence; n = 22, x = 1.72 oz, s = 0.34 oz
52) 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 standard deviation, , of the scores of all subjects.
Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume
that the population has a normal distribution.
53) The amounts (in ounces) of juice in eight randomly selected juice bottles are:
15.6 15.2 15.7 15.5
15.7 15.8 15.6 15.1
Construct a 98% confidence interval for the mean amount of juice in all such bottles.
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation .
Assume that the population has a normal distribution. Round the confidence interval limits to one more decimal place
than is used for the original set of data.
54) The daily intakes of milk (in ounces) for ten randomly selected people were:
31.2 22.9 20.2 13.4 21.3
25.3 15.2 29.7 19.4 22.9
Find a 99% confidence interval for the population standard deviation .
10
Express the null hypothesis and the alternative hypothesis in symbolic form for a test to support this claim. Use the
correct symbol (µ, p, ) for the indicated parameter.
55) Carter Motor Company claims that its new sedan, the Libra, will average better than 27 miles per gallon in the
city. Use µ, the true average mileage of the Libra.
Express the null hypothesis and the alternative hypothesis in symbolic form for a test to reject this claim. Use the correct
symbol (µ, p, ) for the indicated parameter.
56) A researcher claims that 62% of voters favor gun control.
^
Find the value of the test statistic z using z =
p-p
.
pq
n
57) A claim is made that the proportion of children who play sports is less than 0.5, and the sample statistics include
n = 1882 subjects with 30% saying that they play a sport.
Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null
hypothesis (reject the null hypothesis or fail to reject the null hypothesis).
58) With H1 : p > 0.298, the test statistic is z = 0.96.
59) The test statistic in a two-tailed test is z = 1.95.
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.
60) A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard
deviation different from the = 3.3 mg claimed by the manufacturer. Assuming that a hypothesis test to
support this claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the
conclusion in nontechnical terms.
A) There is sufficient evidence to support the claim that the standard deviation is different from 3.3 mg.
B) There is not sufficient evidence to support the claim that the standard deviation is different from 3.3 mg.
C) There is not sufficient evidence to support the claim that the standard deviation is equal to 3.3 mg.
D) There is sufficient evidence to support the claim that the standard deviation is equal to 3.3 mg.
11
Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the
sample has been randomly selected.
61) Heights of men aged 25 to 34 have a standard deviation of 2.9. Use a 0.05 significance level to test the claim that
the heights of women aged 25 to 34 have a different standard deviation. The heights (in inches) of 16 randomly
selected women aged 25 to 34 are listed below. Round the sample standard deviation to five decimal places.
62.13 65.09 64.18 66.72 63.09 61.15 67.50 64.65
63.80 64.21 60.17 68.28 66.49 62.10 65.73 64.72
Assume that a simple random sample has been selected from a normally distributed population and test the given claim.
Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test
statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the
original claim.
62) In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is
made which is supposed to increase the time between failures. Tests on a random sample of 10 modified
components resulted in the following times (in hours) between failures.
518 548 561 523 536
499 538 557 528 563
At the 0.05 significance level, test the claim that for the modified components, the mean time between failures is
greater than 520 hours. Use the P-value method of testing hypotheses.
Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final
conclusion that addresses the original claim.
63) A nationwide study of American homeowners revealed that 64% have one or more lawn mowers. A lawn
equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. Can the
value 0.64 be rejected if a survey of 490 homes in Omaha yields 331 with one or more lawn mowers? Use
= 0.05.
Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have
been randomly selected
64) A researcher finds that of 1000 people who said that they attend a religious service at least once a week, 31
stopped to help a person with car trouble. Of 1200 people interviewed who had not attended a religious service
at least once a month, 22 stopped to help a person with car trouble. At the 0.05 significance level, test the claim
that the two proportions are equal.
65) Seven of 8500 people vaccinated against a certain disease later developed the disease. 18 of 10,000 people
vaccinated with a placebo later developed the disease. Test the claim that the vaccine is effective in lowering the
incidence of the disease. Use a significance level of 0.02.
12
Construct the indicated confidence interval for the difference between population proportions p1 - p2 . Assume that the
samples are independent and that they have been randomly selected.
66) In a random sample of 300 women, 49% favored stricter gun control legislation. In a random sample of 200 men,
27% favored stricter gun control legislation. Construct a 98% confidence interval for the difference between the
population proportions p1 - p2 .
67) In a random sample of 500 people aged 20-24, 22% were smokers. In a random sample of 450 people aged
25-29, 14% were smokers. Construct a 95% confidence interval for the difference between the population
proportions p1 - p2 .
Determine whether the samples are independent or dependent.
68) The effectiveness of a headache medicine is tested by measuring the intensity of a headache in patients before
and after drug treatment. The data consist of before and after intensities for each patient.
A) Independent samples
B) Dependent samples
69) The effectiveness of a new headache medicine is tested by measuring the amount of time before the headache is
cured for patients who use the medicine and another group of patients who use a placebo drug.
A) Dependent samples
B) Independent samples
Test the indicated claim about the means of two populations. Assume that the two samples are independent simple
random samples selected from normally distributed populations. Do not assume that the population standard deviations
are equal. Use the traditional method or P-value method as indicated.
70) A researcher wishes to determine whether the blood pressure of vegetarians is, on average, 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:
Vegetarians
Nonvegetarians
n 1 = 85
n 2 = 75
x1 = 124.1 mmHg
x2 = 138.7 mmHg
s1 = 38.7 mmHg
s2 = 39.2 mmHg
Use a significance level of 0.01 to test the claim that the mean systolic blood pressure of vegetarians is lower
than the mean systolic blood pressure of nonvegetarians. Use the P-value method of hypothesis testing.
13
71) A researcher was interested in comparing the response times of two different cab companies. Companies A and
B were each called at 50 randomly selected times. The calls to company A were made independently of the calls
to company B. The response times for each call were recorded. The summary statistics were as follows:
Company A
Company B
Mean response time
7.6 mins
6.9 mins
Standard deviation
1.4 mins
1.7 mins
Use a 0.02 significance level to test the claim that the mean response time for company A is the same as the
mean response time for company B. Use the P-value method of hypothesis testing.
Construct the indicated confidence interval for the difference between the two population means. Assume that the two
samples are independent simple random samples selected from normally distributed populations. Do not assume that the
population standard deviations are equal.
72) Two types of flares are tested and their burning times are recorded. The summary statistics are given below.
Brand X
Brand Y
n = 35
n = 40
x = 19.4 min
s = 1.4 min
x = 15.1 min
s = 0.8 min
Construct a 95% confidence interval for the differences between the mean burning time of the brand X flare and
the mean burning time of the brand Y flare.
73) A researcher was interested in comparing the amount of time spent watching television by 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 = 12.1 hrs x2 = 13.7 hrs
s1 = 3.9 hrs s2 = 5.2 hrs
n 1 = 14
n 2 = 17
Construct a 99% confidence interval for µ1 - µ2 , the difference between the mean amount of time spent
watching television for women and the mean amount of time spent watching television for men.
Use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that
two dependent samples have been randomly selected from normally distributed populations.
74) Ten different families are tested for the number of gallons of water a day they use before and after viewing a
conservation video. At the 0.05 significance level, test the claim that the mean is the same before and after the
viewing.
Before 33 33 38 33 35 35 40 40 40 31
After
34 28 25 28 35 33 31 28 35 33
14
Construct a confidence interval for µd, the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
75) Using the sample paired data below, construct a 90% confidence interval for the population mean of all
differences x - y.
x 3.6 6.9 4.6 5.2 6.9
y 3.3 5.7 4.2 5.9 4.6
A) -0.37 < µd < 1.77
B) 0.22 < µd < 7.48
C) -0.31 < µd < 1.71
D) -0.07 < µd < 1.47
76) The table below shows the weights of 9 subjects before and after following a particular diet for two months.
Subject A
B
C
D
E
F
G
H
I
Before 168 180 157 132 202 124 190 210 171
After 162 178 145 125 171 126 180 195 163
Construct a 99% confidence interval for the mean difference of the "before" minus "after" weights.
Use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that
two dependent samples have been randomly selected from normally distributed populations.
77) A coach uses a new technique to train gymnasts. 7 gymnasts were randomly selected and their competition
scores were recorded before and after the training. The results are shown below.
Subject A
B
C
D
E
F
G
Before 9.7 9.6 9.5 9.4 9.6 9.6 9.5
After 9.8 9.8 9.5 9.3 9.7 9.9 9.3
Using a 0.01 level of significance, test the claim that the training technique is effective in raising the gymnasts'
scores.
Find the value of the linear correlation coefficient r.
78) x 62 53 64 52 52 54 58
y 158 176 151 164 164 174 162
79) Managers rate employees according to job performance and attitude. The results for several randomly selected
employees are given below.
Performance 59 63 65 69 58 77 76 69 70 64
Attitude
72 67 78 82 75 87 92 83 87 78
15
Use the given data to find the equation of the regression line. Round the final values to three significant digits, if
necessary.
80) Two different tests are designed to measure employee productivity and dexterity. Several employees are
randomly selected and tested with these results.
Productivity 23 25 28 21 21 25 26 30 34 36
Dexterity
49 53 59 42 47 53 55 63 67 75
81) Managers rate employees according to job performance and attitude. The results for several randomly selected
employees are given below.
Performance 59 63 65 69 58 77 76 69 70 64
Attitude
72 67 78 82 75 87 92 83 87 78
82) Match each value of r with the appropriate graph.
r = -1
r = -0.9
r = -0.5
r = 0.5
r = 0.9
r=1
16
83) An 8th grade class develops a linear model that predicts the number of cheerios (a small round cereal) that fit on
the circumference of a plate by using the diameter in inches. Their model is
cheerios = 0.56 + 5.11(diameter).
If the diameter is increased from 4 inches to 14 inches, the predicted number of cheerios will increase by about
A) 72.
B) 10.
C) 21.
D) 51.
E) none of the above.
17
Answer Key
Testname: FINAL EXAM REVIEW MAT1140
1)
2)
3)
4)
5
31
38-42
The approximate age at the center is 50.
5) Restaurant A: 57 sec; 493.98 sec2 ; 22.23 sec
Restaurant B: 77 sec; 727.98 sec2 ; 26.98 sec
There is more variation in the times for restaurant B.
6) Baxter College: mean = 24; median = 24
Banter College: mean = 24.25; median = 24.5
Even though the measures of center are roughly the same, the Banter College values are much more varied than the
Baxter College values.
7) 3.71
8) 2.67 standard deviations below the mean
9) A score of 296.4
10) 61.0
11)
12) Outliers: 1.7 oz, 4.2 oz
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
A
B
A
Not a probability distribution. The sum of the P(x)'s is not 1, since 0.977 1.000.
Not a probability distribution. The sum of the P(x)'s is not 1, since 0.95 1.00.
µ = 3.60
= 1.22
-$4.64
$22,300
18
Answer Key
Testname: FINAL EXAM REVIEW MAT1140
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
49)
50)
51)
52)
53)
54)
55)
µ = 0.80
0.011
0.967
0.969
0.134
0.130
0.115
0.6424
0.9656
0.2776
-0.25
0.13
0.67°
-1.53° , 1.53°
0.1587
0.0643
0.0287
-1.78
1.70
0.019
0.348
0.514
0.0475 < p < 0.105
20.8% < p < 37.0%
6.68 < µ < 13.12
225.9 mg < µ < 242.1 mg
18.475
1.735
0.26 oz < < 0.49 oz
16.9 < < 29.3
15.28 oz < µ < 15.77 oz
3.49 oz < < 12.86 oz
H0 : µ = 27
H1 : µ > 27
56) H0 : p = 0.62
H1 : p 0.62
57)
58)
59)
60)
-17.35
0.1685; fail to reject the null hypothesis
0.0512; fail to reject the null hypothesis
B
61) Test statistic: 2 = 9.2597. Critical values: 2 = 6.262, 27.488. Fail to reject H0 . There is not sufficient evidence to
support the claim that heights of women aged 25 to 34 have a standard deviation different from 2.9 in.
62) H0 : µ = 520 hrs. H1 : µ > 520 hrs. Test statistic: t = 2.612.
0.01 < P-value < 0.025. Reject H0 . There is sufficient evidence to support the claim that the mean is greater than 520
hours.
63) H0 : p = 0.64. H1 : p > 0.64. Test statistic: z = 1.64. P-value: p = 0.0505.
Critical value: z = 1.645. Fail to reject null hypothesis. There is not sufficient evidence to warrant rejection of the claim
that the proportion with lawn mowers in Omaha is 0.64.
19
Answer Key
Testname: FINAL EXAM REVIEW MAT1140
64) H0 : p1 = p2 .
H1 : p1
p2 .
Test statistic: z = 1.93. Critical values: z = ±1.96.
Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two
proportions are equal.
H1 : p1 < p2 .
65) H0 : p1 = p2 .
Test statistic: z = -1.80.
Critical value: z = -2.05.
Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the vaccine is effective in
lowering the incidence of the disease.
66) 0.121 < p1 - p2 < 0.319
67) 0.032 < p1 - p2 < 0.128
68) B
69) B
70) H0 : µ1 = µ2
H1 : µ1 < µ2
Test statistic: t = -2.365
0.005 < P-value < 0.01
Reject H0 . At the 1% significance level, there is sufficient evidence to support the claim that the mean systolic blood
pressure of vegetarians is lower than the mean systolic blood pressure of nonvegetarians.
71) H0 : µ1 = µ2
H1 : µ1 µ2
Test statistic: t = 2.248
0.02 < P-value < 0.05
Do not reject H0 . At the 2% significance level, there is not sufficient evidence to warrant rejection of the claim that the
mean response time for company A is the same as the mean response time for company B.
72) 3.8 min < µX - µY < 4.8 min
73) -6.11 hrs < µ1 - µ2 < 2.91 hrs
74) H0 : µd = 0. H1 : µd 0.
Test statistic t = 2.894. Critical values: t = ±2.262.
Reject H0 . There is sufficient evidence to warrant rejection of the claim that the mean is the same before and after
viewing.
75) A
76) -0.6 < µd < 20.4
77) H0 : µd = 0. H1 : µd < 0
Test statistic t = -0.880. Critical value: t = -3.143.
Fail to reject H0. There is not sufficient evidence to support the claim that the technique is effective in raising the
gymnasts' scores.
78) -0.775
79) 0.863
^
80) y = 5.05 + 1.91x
^
81) y = 11.7 + 1.02x
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Answer Key
Testname: FINAL EXAM REVIEW MAT1140
82)
r = -1
r = -0.9
r = -0.5
r = 0.5
r = 0.9
r=1
d
b
f
a
e
c
83) D
21