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Sample Final Review I
Math 1107
DeMaio
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
In a large class, the professor has each person toss a coin several times and calculate the proportion of his or her tosses
that were heads. The students then report their results, and the professor plots a histogram of these several proportions.
Use the 68-95-99.7 Rule to provide the appropriate response.
1) If the students toss the coin 200 times each, about 68% should have proportions between what two
numbers?
1)
A) 0.4975 and 0.5025
B) 0.34 and 0.67
C) 0.465 and 0.535
D) 0.16 and 0.84
E) 0.035 and 0.07
Find the specified probability, from a table of Normal probabilities.
2) Based on past experience, a bank believes that 4% of the people who receive loans will not make
payments on time. The bank has recently approved 300 loans. What is the probability that over 6%
of these clients will not make timely payments?
A) 0.904
B) 0.096
C) 0.038
D) 0.962
E) 0.017
3) When a truckload of oranges arrives at a packing plant, a random sample of 125 is selected and
examined. The whole truckload will be rejected if more than 8% of the sample is unsatisfactory.
Suppose that in fact 12% of the oranges on the truck do not meet the desired standard. What's the
probability that the shipment will be rejected?
A) 0.0838
B) 0.9479
C) 0.0521
D) 0.1676
2)
3)
E) 0.9162
Answer the question.
4) A candy company claims that 16% of the jelly beans in its spring mix are pink. Suppose that the
candies are packaged at random in bags containing about 400 jelly beans. A class of students
opens several bags, counts the various colors of jelly beans, and calculates the proportion that are
pink. In one bag, the students found 13% of the jelly beans were pink. Is this an unusually small
proportion of pink jelly beans? Explain your response.
A) This is a very unusual result. It is 0.05 standard deviations below the mean.
B) This is not an unusual result. It is only 1.64 standard deviations below the mean.
C) This is an extremely unlikely result. It is 0.22 standard deviations below the mean.
D) This is not an unusual result. It is only 0.05 standard deviations below the mean.
E) This is a very unusual result. It is 0.08 standard deviations below the mean.
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4)
Find the mean of the data.
5) The local Tupperware dealers earned the following commissions, in dollars, last month.
$2243.95
$4494.07
$1759.41
$2934.80
$2850.64
$4330.66
$1333.14
$2643.61
$2451.82
5)
$3927.47
Round your answer to the nearest cent.
A) $2896.96
B) $2934.80
C) $3218.84
D) $2890.96
E) $3621.20
Find the median of the data.
6) The number of cars passing through a bank drive-up line during each 15-minute period was
recorded. The results are shown below.
6)
27 29 27 30
30 27 32 29
37 33 33 31
26 33 27 22
17 29 29 29
A) 28.85 cars
B) 33 cars
C) 30 cars
D) 29 cars
E) 27 cars
Solve the problem.
7) The ages of the 21 members of a track and field team are listed below. Find the standard deviation.
15
24
28
18
24
28
A) 6.6
18
25
30
19
25
32
22
26
33
23
26
40
7)
24
27
42
B) 6.5
C) 6.4
D) 6.7
E) 6.3
Use summary statistics to answer the question.
8) Here are some statistics for the annual Wildcat golf tournament: lowest score = 60, mean
score = 93, median = 101, range = 90, IQR = 96, Q1 = 37, standard deviation = 12. Suppose it was
very windy and all the golfers' scores went up by 7 strokes. Tell the new value for each of the
summary statistics.
A) Lowest score: 67, mean: 100, median: 108, range: 83, IQR: 96, Q1: 44, SD: 12
B) Lowest score: 67, mean: 100, median: 108, range: 90, IQR: 96, Q1: 44, SD: 12
C) Lowest score: 67, mean: 100, median: 108, range: 83, IQR: 103, Q1: 44, SD: 12
D) Lowest score: 67, mean: 93, median: 101, range: 83, IQR: 96, Q1: 44, SD: 12
E) Lowest score: 67, mean: 100, median: 108, range: 83, IQR: 96, Q1: 44, SD: 19
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8)
9) Here are some summary statistics for the recent English exam: lowest score = 33, mean score = 68,
median = 82.2, range = 77, IQR = 59, Q1 = 27, standard deviation = 8.3. Between what two values
are the middle 50% of the scores found?
9)
A) 20.55 and 61.65
B) 33 and 110
C) 17 and 51
D) 27 and 86
E) 68 and 82.2
Solve the problem.
10) A town's snowfall in December averages 19 inches with a standard deviation of 8 inches while in
February, the average snowfall is 43 inches with a standard deviation of 14 inches. In which
month is it more likely to snow 32 inches? Explain.
11
13
from the mean while snowfall of 32 inches is from
A) December. Snowfall of 32 inches is
14
8
10)
the mean in February.
B) It is equally likely in either month. One can't predict Mother Nature.
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13
C) February. Snowfall of 32 inches is from the mean while snowfall of 32 inches is
from
14
8
the mean in December.
D) December. Snowfall of 32 inches is -
13
11
from the mean while snowfall of 32 inches is
from
8
14
the mean in February.
E) February. Snowfall of 32 inches is
11
13
from the mean while snowfall of 32 inches is from
14
8
the mean in December.
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion.
11) When 293 college students are randomly selected and surveyed, it is found that 114 own a car.
Construct a 99% confidence interval for the percentage of all college students who own a car.
11)
A) (34.2%, 43.6%)
B) (31.6%, 46.2%)
C) (17.4%, 60.4%)
D) (32.3%, 45.5%)
E) (33.3%, 44.5%)
Solve the problem.
12) For a recent English exam, use the Normal model N(73, 9.2) to find the percent of scores under 58.
Round to the nearest tenth of a percent.
A) 5.2%
B) 1.63%
C) 95.8%
D) 94.8%
12)
E) 4.2%
Solve the problem. Round to the nearest tenth.
13) Based on the Normal model for snowfall in a certain town N(57, 8), how many inches of snow
would represent the 75th percentile?
A) 62.4 inches
B) 51.6 inches
C) 65 inches
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D) 42.8 inches
E) 49 inches
13)
14) Based on the Normal model for car speeds on an old town highway N(77, 9.1), what is the cutoff
value for the lowest 30% of the speeds?
14)
A) about 81.7 mph
B) about 23.1 mph
C) about 53.9 mph
D) about 60.9 mph
E) about 72.3 mph
Solve the problem.
15) In a survey of American women who were asked to name their favorite color, 18% said blue, 15%
said red, 15% said green, 12% said yellow, 13% said black, and the rest named another color. If you
pick a survey participant at random, what is the probability that she named another color?
A) 0.27
B) 0.78
C) 0.24
D) 0.73
15)
E) 0.20
Find the indicated probability.
16) The probability that Luis will pass his statistics test is 0.40. Find the probability that he will fail his
statistics test.
A) 2.50
B) 0.67
C) 0.20
16)
D) 0.60
17) A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 12 wood
and 13 graphite are defective and one racket is randomly selected from the sample, find the
probability that the racket is wood or defective.
17)
A) 0.125
B) 0.56
C) 0.565
D) There is insufficient information to answer the question.
18) The table below describes the smoking habits of a group of asthma sufferers.
Occasional Regular Heavy
Nonsmoker
smoker
smoker smoker Total
Men
345
40
78
50
513
Women
417
36
72
37
562
Total
762
76
150
87
1075
18)
If one of the 1075 people is randomly selected, find the probability of getting a regular or heavy
smoker.
A) 0.540
B) 0.220
C) 0.140
D) 0.119
19) A study conducted at a certain college shows that 61% of the school's graduates find a job in their
chosen field within a year after graduation. Find the probability that 9 randomly selected graduates
all find jobs in their chosen field within a year of graduating.
A) 0.012
B) 0.019
C) 0.148
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D) 5.490
19)
Provide an appropriate response.
20) Students in a political science course were asked to describe their politics as "Liberal", "Moderate",
or "Conservative." Here are the results:
Politics
Female
Male
Total
Liberal
37
53
90
Moderate
25
55
80
Conservative
11
29
40
20)
Total
73
137
210
What percent of all "Moderates" in the class are male?
A) 68.8%
B) 26.2%
C) 38.1%
D) 40.1%
E) 31.3%
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final
conclusion that addresses the original claim.
21) According to a recent poll 53% of Americans would vote for the incumbent president. If a
random sample of 100 people results in 45% who would vote for the incumbent, test the
claim that the actual percentage is 53%. Use a 0.10 significance level.
21)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the P-value for the indicated hypothesis test.
22) A manufacturer claims that fewer than 6% of its fax machines are defective. In a random sample of
97 such fax machines, 5% are defective. Find the P-value for a test of the manufacturer's claim.
A) 0.1591
B) 0.3264
C) 0.3409
22)
D) 0.1736
Construct the indicated confidence interval for the difference between the two population means. Assume that the
assumptions and conditions for inference have been met.
23) Two types of flares are tested for their burning times (in minutes) and sample results are given
below.
Brand X
Brand Y
n = 35
n = 40
x = 19.4
s = 1.4
x = 15.1
s = 0.8
Construct a 95% confidence interval for the difference m X - m Y based on the sample data.
A) (3.2, 5.4)
B) (3.6, 5.0)
C) (3.8, 4.8)
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D) (3.5, 5.1)
E) (-4.7, -3.9)
23)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Assume that the assumptions and conditions for inference with a two-sample t-test are met. Test the indicated claim
about the means of the two populations.
24) A researcher wishes to determine whether people with high blood pressure can reduce
their blood pressure by following a particular diet. Use the sample data below to test the
claim that the treatment population mean m 1 is smaller than the control population mean m
2. Test the claim using a significance level of 0.01.
Treatment Group
Control Group
n 1 = 85
n 2 = 75
x1 = 189.1
x2 = 203.7
s 1 = 38.7
s 2 = 39.2
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24)
Answer Key
Testname: SAMPLE FINAL 1
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C
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E
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A
H0: p = 0.53. H1: p ≠ 0.53. Test statistic: z = -1.60. P-value: p = 0.0548.
Critical value: z = ±1.645. Fail to reject null hypothesis. There is not sufficient evidence to warrant rejection of the claim
that the actual percentage is 53%.
22) C
23) C
24) H0: m 1- m 2 = 0
HA: m 1 - m 2 < 0
Test statistic t = -2.365, P-value = 0.00963, DF = 155.01
Reject the null hypothesis. There is sufficient evidence to support the claim that the treatment population mean m 1 is
smaller than the control population mean m 2.
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