Download Chap 18 and 19 in cl.. - College of Science and Mathematics

Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Describe the indicated sampling distribution model.
1) 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.
1)
A) N(8%, 0.3%)
B) Binom(600, 8%)
C) N(92%, 1.1%)
D) There is not enough information to describe the distribution.
E) N(8%, 1.1%)
Answer the question.
2) A candy company claims that 8% of the jelly beans in its spring mix are pink. Suppose that the
candies are packaged at random in small bags containing about 50 jelly beans. A class of students
opens several bags, counts the various colors of jelly beans, and calculates the proportion that are
pink. Is it appropriate to use a Normal model to describe the distribution of the proportion of pink
jelly beans?
2)
A) A Normal model is not appropriate because the sample size is not large enough to satisfy the
success/failure condition. For this sample size, np = 4 < 10.
B) A Normal model is not appropriate because the population distribution is not Normal.
C) A Normal model is not appropriate because the sample size, 50, is larger than 10% of the
population of all bags of jelly beans.
D) A Normal model is appropriate because the samples are random and independent. Also, the
sample size, 50, is less than 10% of the population.
E) A Normal model is appropriate because the 50 bags of jelly beans can be thought of as a
random sample of bags and are fewer than 10% of the population of all bags. The
success/failure condition is also satisfied because n = 50 ≥ 10.
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.
3) If the students toss the coin 200 times each, about 68% should have proportions between what two
numbers?
3)
A) 0.16 and 0.84
B) 0.035 and 0.07
C) 0.4975 and 0.5025
D) 0.34 and 0.67
E) 0.465 and 0.535
Find the specified probability, from a table of Normal probabilities.
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
B) 0.9578
C) 0.0422
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D) 0.0239
E) 0.0478
4)
5) 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. What's the
probability that the shipment will be accepted anyway?
A) 0.0827
B) 0.2846
C) 0.8577
D) 0.1423
5)
E) 0.9173
Answer the question.
6) 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.
6)
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 not an unusual result. It is only 0.05 standard deviations below the mean.
D) This is a very unusual result. It is 0.08 standard deviations below the mean.
E) This is an extremely unlikely result. It is 0.22 standard deviations below the mean.
Describe the indicated sampling distribution model.
7) Suppose that the national mean weight for a three-year-old girl is 30 pounds with a standard
deviation of 3 pounds. A pediatric office takes a random sample of 100 three-year-old girls,
records their weights, and finds the mean. Describe the sampling distribution model of this mean.
7)
A) N(30, 0.03)
B) N(30, 0.3)
C) N(30, 3)
D) There is not enough information to describe the distribution.
E) Binom(30, 3)
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.
8) If we imagine all the possible random samples of 100 students at this university, 68% of the
samples should have means between what two numbers?
8)
A) $2260.00 and $2740.00
B) $2380.00 and $2620.00
C) $2380.00 and $2740.00
D) $2140.00 and $2860.00
E) $1300 and $2700
Find the specified probability, from a table of Normal probabilities.
9) 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
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) 0.5161
B) 0.1528
C) 0.547
D) 0.080
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E) 0.3043
9)
10) 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 at least $58 on dinner?
A) 0.9868
B) 0.5879
C) 0.4121
D) 0.0132
10)
E) 0.0562
Find the margin of error for the given confidence interval.
11) A survey found that 89% of a random sample of 1024 American adults approved of cloning
endangered animals. Find the margin of error for this survey if we want 90% confidence in our
estimate of the percent of American adults who approve of cloning endangered animals.
A) 4.85%
B) 1.61%
C) 5.78%
D) 1.92%
11)
E) 16.5%
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion.
12) 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.
12)
A) (31.9%, 42.8%)
B) (17.8%, 56.8%)
C) (26.7%, 47.9%)
D) (30.1%, 44.5%)
E) (30.8%, 43.8%)
13) Of 149 randomly selected adults, 32 were found to have high blood pressure. Construct a 95%
confidence interval for the percentage of all adults who have high blood pressure.
13)
A) (13.6%, 29.3%)
B) (15.9%, 27.0%)
C) (14.9%, 28.1%)
D) (12.8%, 30.2%)
E) (11.7%, 31.3%)
14) 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.
A) (2.43%, 6.71%)
B) (2.64%, 6.50%)
C) (2.95%, 6.20%)
D) (3.21%, 5.94%)
E) (3.4%, 5.8%)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
15) A mayoral election race is tightly contested. In a random sample of 1100 likely voters, 572
said that they were planning to vote for the current mayor. Based on this sample, would
you claim with 95% confidence that the mayor will win a majority of the votes? Explain.
15)
16) A mayoral election race is tightly contested. In a random sample of 1300 likely voters, 689
said that they were planning to vote for the current mayor. Based on this sample, would
you claim with 95% confidence that the mayor will win a majority of the votes? Explain.
16)
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14)
Use critical thinking to address the key issue.
17) 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?
17)
18) "7 out of 10 dentists recommend Brand X toothpaste". This finding is based on the results
of a survey of 10 randomly selected dentists. What is wrong with this survey?
18)
19) "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?
19)
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Answer Key
Testname: SAMPLING DISTRIBUTION AND CONFIDENCE INTERVAL QUESTIONS
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E
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E
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B
No; in the sample 52% said that they were planning to vote for the current mayor. However the margin of error (with
95% confidence) is greater than 2% (it is 3.0 percentage points). So we cannot be 95% confident that the mayor will
win more than 50% of the votes. The 95% confidence interval for the population proportion includes some values
smaller than 50%.
Yes; in the sample 53% said that they were planning to vote for the current mayor and the margin of error (with 95%
confidence) is smaller than 3% (it is 2.7 percentage points). So we can be 95% confident that the mayor will win more
than 50% of the votes. The 95% confidence interval for the population proportion lies entirely above 50%.
This is not a random sample. The survey is based on voluntary, self-selected responses and therefore has serious
potential for bias.
The sample was too small.
The sample is biased. College students are not representative of the U.S. population as a whole.
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