Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Write the null and alternative hypotheses you would use to test the following situation.
1) 5% of trucks of a certain model have needed new engines after being driven between 0 and 100
miles. The manufacturer hopes that the redesign of one of the engineʹs components has solved this
problem.
A) H0 : p = 0.05
1)
HA: p < 0.05
B) H0 : p > 0.05
HA: p = 0.05
C) H0 : p = 0.05
HA: p > 0.05
D) H0 : p < 0.05
HA: p > 0.05
E) H0 : p < 0.05
HA: p = 0.05
2) At a local university, only 62% of the original freshman class graduated in four years. Has this
percentage changed?
A) H0 : p ≠ 0.62
2)
HA: p = 0.62
B) H0 : p = 0.62
HA: p < 0.62
C) H0 : p < 0.62
HA: p = 0.62
D) H0 : p < 0.62
HA: p > 0.62
E) H0 : p = 0.62
HA: p ≠ 0.62
Find the specified probability, from a table of Normal probabilities.
3) Researchers believe that 6% of children have a gene that may be linked to a certain childhood
disease. In an effort to track 50 of these children, researchers test 950 newborns for the presence of
this gene. What is the probability that they find enough subjects for their study?
A) 0.7912
B) 0.8507
C) 0.8315
D) 0.337
E) 0.1685
4) 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 11% of the oranges on the truck do not meet the desired standard. Whatʹs the
probability that the shipment will be accepted anyway?
A) 0.2846
B) 0.9173
C) 0.8577
D) 0.1423
E) 0.0827
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3)
4)
5) The weight of crackers in a box is stated to be 16 ounces. The amount that the packaging machine
puts in the boxes is believed to have a Normal model with mean 16.15 ounces and standard
deviation 0.3 ounces. What is the probability that the mean weight of a 50-box case of crackers is
above 16 ounces?
A) 0.0004
B) 0.9996
C) 0.9994
D) 0.0002
E) 0.9998
5)
6) The number of hours per week that high school seniors spend on homework is normally
distributed, with a mean of 10 hours and a standard deviation of 3 hours. 60 students are chosen at
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random. Let y represent the mean number of hours spent on homework for this group. Find the
probability that y is between 9.8 and 10.4.
A) 0.547
B) 0.080
C) 0.1528
D) 0.5161
E) 0.3043
Write the null and alternative hypothesis.
7) You want to see if the number of minutes cell phone users use each month has changed from its
mean of 120 minutes 2 years ago. You take a random sample of 100 cell phone users and find an
average of 135 minutes used.
A) H0 : μ = 120
7)
HA: μ > 120
B) H0 : μ = 135
HA: μ > 135
C) H0 : μ = 120
HA: μ < 120
D) H0 : μ = 120
HA: μ ≠ 120
E) H0 : μ = 135
HA: μ ≠ 135
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.
8) If the students toss the coin 200 times each, about 68% should have proportions between what two
8)
numbers?
A) 0.465 and 0.535
B) 0.4975 and 0.5025
C) 0.16 and 0.84
D) 0.035 and 0.07
E) 0.34 and 0.67
9) If the students toss the coin 100 times each, about 95% should have proportions between what two
numbers?
A) 0.2375 and 0.7375
B) 0.025 and 0.975
C) 0.1 and 0.15
D) 0.4 and 0.6
E) 0.49 and 0.51
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9)
Create a 95% confidence interval for the given data.
10) A company hopes to improve its engines, setting a goal of no more than 3% of customers using
their warranty on defective engine parts. A random survey of 1200 customers found only 20 with
complaints. Create a 95% confidence interval for the true level of warranty users among all
customers.
A) Based on the data, we are 95% confident the proportion of warranty users is between 0.9%
and 2.4%. Therefore, the company has met its goal.
B) Based on the data, we are 95% confident the proportion of warranty users is between 0% and
2.4%. Therefore, the company has met its goal.
C) Based on the data, we are 95% confident the proportion of warranty users is between 1% and
3%. Therefore, the company has met its goal.
D) Based on the data, we are 95% confident the proportion of warranty users is between 0.9%
and 3.8%. Therefore, the company has not met its goal.
E) Based on the data, we are 95% confident the proportion of warranty users is between 2.0%
and 2.4%. Therefore, the company has met its goal.
Construct the requested confidence interval from the supplied information.
11) A sample of 81 statistics students at a small college had a mean mathematics ACT score of 26 with
a standard deviation of 6. Find a 95% confidence interval for the mean mathematics ACT score for
all statistics students at this college.
A) (25.9, 26.1)
B) (24.7, 27.3)
C) (25.3, 26.1)
D) (25.3, 26.7)
E) (78.6, 83.4)
12) Among a sample of 65 students selected at random from one college, the mean number of siblings
is 1.3 with a standard deviation of 1.1. Find a 95% confidence interval for the mean number of
siblings for all students at this college.
A) (63.07, 66.93)
B) (1.03, 1.57)
C) (1.16, 1.33)
D) (1.16, 1.44)
E) (1.27, 1.33)
10)
11)
12)
At a large university, students have an average credit card debt of $2500, with a standard deviation of $1200. A random
sample of students is selected and interviewed about their credit card debt. Use the 68-95-99.7 Rule to answer the
question about the mean credit card debt for the students in this sample.
13) If we imagine all the possible random samples of 100 students at this university, 68% of the
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samples should have means between what two numbers?
A) $1300 and $2700
B) $2140.00 and $2860.00
C) $2260.00 and $2740.00
D) $2380.00 and $2740.00
E) $2380.00 and $2620.00
14) If we imagine all the possible random samples of 250 students at this university, 95% of the
samples should have means between what two numbers?
A) $250.00 and $2575.89
B) $2348.22 and $2651.78
C) $2272.33 and $2727.67
D) $300 and $4900
E) $250.00 and $2651.78
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14)
Determine the margin of error in estimating the population parameter.
15) Based on a sample of 39 randomly selected years, a 90% confidence interval for the mean annual
precipitation in one city is from 42.8 inches to 45.2 inches.
A) 0.32 inches
B) 2.4 inches
C) 1.2 inches
D) 0.10 inches
E) Not enough information is given.
Classify the hypothesis test as lower-tailed, upper-tailed, or two-sided.
16) At one school, the average amount of time that tenth-graders spend watching television each
week is 21.6 hours. The principal introduces a campaign to encourage the students to watch less
television. One year later, the principal wants to perform a hypothesis test to determine whether
the average amount of time spent watching television per week has decreased from the previous
mean of 21.6 hours.
A) Two-sided
B) Lower-tailed
C) Upper-tailed
Interpret the confidence interval.
17) Data collected by child development scientists produced the following 90% confidence interval for
the average age (in months) at which children say their first word: 10.4 < μ(age) < 13.8.
A) 90% of the children in this sample said their first word when they were between 10.4 and 13.8
months old.
B) Based on this sample, we can say, with 90% confidence, that the mean age at which children
say their first word is between 10.4 and 13.8 months.
C) If we took many random samples of children, about 90% of them would produce this
confidence interval.
D) We are 90% sure that a child will say his first word when he is between 10.4 and 13.8 months
old.
E) We are 90% sure that the average age at which children in this sample said their first word
was between 10.4 and 13.8 months.
Describe the indicated sampling distribution model.
18) Based on past experience, a bank believes that 8% of the people who receive loans will not make
payments on time. The bank has recently approved 600 loans. Describe the sampling distribution
model of the proportion of clients in this group who may not make timely payments.
A) Binom(600, 8%)
B) N(92%, 1.1%)
C) There is not enough information to describe the distribution.
D) N(8%, 1.1%)
E) N(8%, 0.3%)
19) Statistics from a weather center indicate that a certain city receives an average of 25 inches of snow
each year, with a standard deviation of 7 inches. Assume that a Normal model applies. A student
lives in this city for 4 years. Let y represent the mean amount of snow for those 4 years. Describe
the sampling distribution model of this sample mean.
A) N(25, 7)
B) Binom(25, 7)
C) N(25, 3.5)
D) There is not enough information to describe the distribution.
E) N(25, 1.75)
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19)
Use a hypothesis test to test the given claim.
20) Is the mean lifetime of particular type of car engine greater than 220,000 miles? To test this claim, a
sample of 23 engines is measured, yielding an average of 226,450 miles and a standard deviation of
11,500 miles. Use a significance level of 0.01.
A) Reject the null hypothesis of μ=220,000 with a P-value of 0.01338. There is sufficient
evidence that the engines last longer than 220,000 miles.
B) Reject the null hypothesis of μ=220,000 with a P-value of 0.00669. There is sufficient
evidence that the engines last longer than 220,000 miles.
C) Fail to reject the null hypothesis of μ=220,000 with a P-value of 0.9933. There isnot sufficient
evidence that the engines last longer than 220,000 miles.
D) Fail to reject the null hypothesis with a P-value of 0.07352.There is not sufficient evidence
that the engines last longer than 220,000 miles.
E) There is not enough information to perform the test.
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20)
Answer Key
Testname: SAMPLE TEST 3 PART 2
1) A
2) E
3) C
4) D
5) E
6) A
7) D
8) A
9) D
10) A
11) B
12) B
13) E
14) B
15) C
16) B
17) B
18) D
19) C
20) B
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