Download sample proportion qu.. - College of Science and Mathematics

Exam
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 100 times each, about 95% should have proportions between what two
numbers?
1)
A) 0.1 and 0.15
B) 0.49 and 0.51
C) 0.2375 and 0.7375
D) 0.025 and 0.975
E) 0.4 and 0.6
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) 0.096
B) 0.038
C) 0.962
D) 0.017
E) 0.904
3) Assume that 20% of students at a university wear contact lenses. We randomly pick 200 students.
What is the probability that more than 22% of this sample wear contact lenses?
A) 0.520
B) 0.760
C) 0.239
D) 0.480
B) 0.9578
C) 0.0478
D) 0.0422
B) 0.0571
C) 0.9137
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D) 0.1142
4)
E) 0.0239
5) A candy company claims that its jelly bean mix contains 15% blue jelly beans. Suppose that the
candies are packaged at random in small bags containing about 200 jelly beans. What is the
probability that a bag will contain more than 11% blue jelly beans?
A) 0.9429
3)
E) 0.707
4) A candy company claims that its jelly bean mix contains 15% blue jelly beans. Suppose that the
candies are packaged at random in small bags containing about 200 jelly beans. What is the
probability that a bag will contain more than 20% blue jelly beans?
A) 0.9761
2)
E) 0.894
5)
Answer the question.
6) In a large class, the professor has each person toss a coin 200 times and calculate the proportion of
his or her tosses that were tails. The students then report their results, and the professor records
the proportions. One student claims to have tossed her coin 200 times and found 60% tails. What
do you think of this claim? Explain your response.
6)
A) This is a typical result. Her proportion is only 2.83 standard deviations above the mean.
B) This is a fairly unusual result. Her proportion is about 2.83 standard deviations above the
mean.
C) This is an extremely unlikely result. Her proportion is about 200 standard deviations above
the mean.
D) This is a typical result. Her proportion is only 2.00 standard deviations above the mean.
E) This is a fairly unusual result. Her proportion is about 2.00 standard deviations above the
mean.
Find the specified probability, from a table of Normal probabilities.
7) 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) 0.9998
B) 0.9994
C) 0.0004
D) 0.9996
E) 0.0002
8) A restaurant's receipts show that the cost of customers' dinners has a skewed distribution with a
mean of $54 and a standard deviation of $18. What is the probability that the next 100 customers
will spend an average of less than $56 on dinner?
A) 0.8665
B) 0.1552
C) 0.4558
D) 0.1335
E) 0.5442
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Use critical thinking to address the key issue.
9) A questionnaire is sent to 10,000 persons. 5,000 responded to the questionnaire. 3,000 of
the respondents say that they "love chocolate ice cream". We conclude that 60% of people
love chocolate ice cream. What is wrong with this survey?
9)
10) An airline company advertises that 100% of their flights are on time after checking 5
randomly selected flights and finding that these 5 were on time.
10)
11) A researcher published this survey result: "74% of people would be willing to spend 10
percent more for energy from a non-polluting source". The survey question was
announced on a national radio show and 1,200 listeners responded by calling in. What is
wrong with this survey?
11)
12) "38% of adults in the United States regularly visit a doctor". This conclusion was reached
by a college student after she had questioned 520 randomly selected members of her
college. What is wrong with her survey?
12)
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8)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion.
13) A survey of 300 union members in New York State reveals that 112 favor the Republican candidate
for governor. Construct a 98% confidence interval for the percentage of all New York State union
members who favor the Republican candidate.
13)
A) (30.1%, 44.5%)
B) (17.8%, 56.8%)
C) (26.7%, 47.9%)
D) (31.9%, 42.8%)
E) (30.8%, 43.8%)
14) Of 81 adults selected randomly from one town, 64 have health insurance. Construct a 90%
confidence interval for the percentage of all adults in the town who have health insurance.
14)
A) (67.4%, 90.7%)
B) (68.5%, 89.6%)
C) (71.6%, 86.5%)
D) (73.0%, 85.0%)
E) (70.1%, 87.9%)
15) A study involves 634 randomly selected deaths, with 29 of them caused by accidents. Construct a
98% confidence interval for the percentage of all deaths that are caused by accidents.
15)
A) (2.95%, 6.20%)
B) (2.43%, 6.71%)
C) (3.21%, 5.94%)
D) (2.64%, 6.50%)
E) (3.4%, 5.8%)
Write the null and alternative hypotheses you would use to test the following situation.
16) A mayor is concerned about the percentage of city residents who express disapproval of his job
performance. His political committee pays for a newspaper ad, hoping that it will keep the
disapproval rate below 17%. They will use a follow-up poll to assess the ad's effectiveness.
A) H0: p = 0.17
HA: p > 0.17
B) H0: p > 0.17
HA: p = 0.17
C) H0: p < 0.17
HA: p = 0.17
D) H0: p > 0.17
HA: p < 0.17
E) H0: p = 0.17
HA: p < 0.17
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17) 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 engine's components has solved this
problem.
17)
A) H0: p = 0.05
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
18) The U.S. Department of Labor and Statistics released the current unemployment rate of 5.3% for
the month in the U.S. and claims the unemployment has not changed in the last two months.
However, the state's statistics reveal that there is a change in U.S. unemployment rate. What are the
null and alternative hypotheses?
A) H0: p ≠ 0.053
HA: p = 0.053
B) H0: p = 0.053
HA: p > 0.053
C) H0: p < 0.053
HA: p = 0.053
D) H0: p = 0.053
HA: p ≠ 0.053
E) H0: p > 0.053
HA: p < 0.053
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Provide an appropriate response.
19) A state university wants to increase its retention rate of 4% for graduating students from the
previous year. After implementing several new programs during the last two years, the university
reevaluated its retention rate using a random sample of 352 students and found the retention rate
at 5%. Test an appropriate hypothesis and state your conclusion. Be sure the appropriate
assumptions and conditions are satisfied before you proceed.
19)
A) H0 : p = 0.04; HA: p < 0.04; z = 1.07; P-value = 0.8577. This data shows that more than 4% of
students are retained; therefore, the university should continue with the new programs.
B) H0 : p = 0.04; HA: p > 0.04; z = -1.07; P-value = 0.1423. This data does not show that more than
4% of students are retained; the university should not continue with the new programs.
C) H0 : p = 0.04; HA: p < 0.04; z = -1.07; P-value = 0.8577. This data shows that more than 4% of
students are retained; the university should continue with the new programs.
D) H0 : p = 0.04; HA: p > 0.04; z = 0.96; P-value = 0.1685. This data does not show that more than
4% of students are retained; the university should not continue with the new programs.
E) H0 : p = 0.04; HA: p ≠ 0.04; z = 1.07; P-value = 0.2846. This data does not show that more than
4% of students are retained; the university should not continue with the new programs.
20) A survey investigates whether the proportion of 8% for employees who commute by car to work is
higher than it was five years ago. A test on employee commuting by car was done on a random
sample of 1000 employees, and found car commuting to be 12%. Test an appropriate hypothesis
and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before
you proceed.
A) H0 : p = 0.08; HA: p > 0.08; z = -4.66; P-value > 0.00001. This data shows a proportion in car
commuting greater than 8%.
B) H0 : p = 0.08; HA: p > 0.08; z = 4.66; P-value < 0.00001. This data shows a proportion in car
commuting greater than 8%.
C) H0 : p = 0.08; HA: p < 0.08; z = 4.66; P-value < 0.99999. This data does not show a proportion
in car commuting greater than 8%.
D) H0 : p = 0.08; HA: p < 0.08; z = -4.66; P-value > 0.99999. This data does not show a proportion
in car commuting greater than 8%.
E) H0 : p = 0.08; HA: p ≠ 0.08; z = 4.66; P-value < 0.99999. This data does not show a proportion in
car commuting greater than 8%.
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21) The U.S. Department of Labor and Statistics released the current unemployment rate of 5.3% for
the month in the U.S. and claims the unemployment has not changed in the last two months.
However, the states statistics reveal that there is a decrease in the U.S. unemployment rate. A test
on unemployment was done on a random sample size of 1000 and found unemployment at 3.8%.
Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions
and conditions are satisfied before you proceed.
A) H0 : p = 0.053; HA: p < 0.053; z = 2.12; P-value = 0.017. This data does not show that the
unemployment rate has decreased in the last two months.
B) H0 : p = 0.053; HA: p > 0.053; z = -2.12; P-value = 0.983. This data does not show that the
unemployment rate has decreased in the last two months.
C) H0 : p = 0.053; HA: p > 0.053; z = 2.12; P-value = 0.983. This data shows that the
unemployment rate has decreased in the last two months.
D) H0 : p = 0.053; HA: p < 0.053; z = -2.12; P-value = 0.017. This data shows that the
unemployment rate has decreased in the last two months.
E) H0 : p = 0.053; HA: p ≠ 0.053; z = -2.12; P-value = 0.034. This data shows that the
unemployment rate has decreased in the last two months.
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Answer Key
Testname: SAMPLE PROPORTION QUESTIONS
1)
2)
3)
4)
5)
6)
7)
8)
9)
E
B
C
E
A
B
A
A
This is not a random sample. The survey is based on voluntary, self-selected responses and therefore has serious
potential for bias.
10) The sample was too small.
11) This is not a random sample. The survey is based on voluntary, self-selected responses and therefore has serious
potential for bias.
12) The sample is biased. College students are not representative of the U.S. population as a whole.
13)
14)
15)
16)
17)
18)
19)
20)
21)
E
C
D
E
B
D
D
B
D
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