Chapter 9
STT 200 – STATISTICAL METHODS
HOMEWORK ASSIGNMENT NUMBER 5
DUE DATE: WEDNESDAY NOVEMBER 25, 2015
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Chapter 9
1. When a truckload of apples arrives at a packing plant, a random sample of 125 is selected and
examined for bruises, discoloration, and other defects. The whole truckload will be rejected if
more than 8% of the sample is unsatisfactory. Suppose that in fact 12% of the apples on the truck
do not meet the desired standard. What’s the probability that the shipment will be accepted
anyway?
A. 0.029065
B. 0.970935
C. 0.00084
D. 0.9156
E. 0.08437
QUESTIONS 2 – 3
It’s believed that 8% of children have a gene that may be linked to juvenile diabetes. Researchers
hoping to track 40 of these children for several years test 542 newborns for the presence of this
gene.
2. The sampling distribution of the proportion of children with gene linked to juvenile diabetes is
best described as
A. N(0.01165, 0.08)
B. N(0.08, 0.01165)
C. N(40, 542)
D. N(0.08, 0.000136)
E. N(0.000136, 0.01165)
3. What is the probability that they find enough subjects for their study?
A. 0.2974
B. 0.0738
C. 0.9200
D. 0.7026
E. 0.0800
QUESTIONS 4 – 6
The weight of potato chips in a medium-size bag is stated to be 12 ounces. The amount that the
packaging machine puts in these bags is believed to have a Normal model with mean 12.1
ounces and standard deviation 0.09 ounces.
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4. What fraction of all bags sold are underweight?
A. 0.9804
B. 0.0478
C. 0.8667
D. 0.0900
E. 0.1333
5. Some of the chips are sold in “bargain packs” of 5 bags. What’s the probability that none of
the 5 is underweight?
A. 0.8630
B. 0.1434
C. 0.5108
D. 0.4892
E. 0.1333
6. What’s the probability that the mean weight of the 5 bags is below the stated amount?
A. 0.9935
B. 0.0478
C. 0.0065
D. 0.4892
E. 0.1333
7. Assessment records indicate that the value of homes in a small city is skewed right, with a
mean of $140,000 and standard deviation of $60,000. To check the accuracy of the assessment
data, officials plan to conduct a detailed appraisal of 100 homes selected at random. What is the
probability that the mean home value is between $128,000 and $152,000? (Hint: 68 – 95 –
99.7% Rule)
A. 0.320
B. 0.0857
C. 0.997
D. 0.950
E. 0.680
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QUESTIONS 8 – 9
Information on a packet of seeds claims that the germination rate is 94%. The packet contains
160 seeds. Let p̂ represent the proportion of seeds in the packet that will germinate.
8. The sampling distribution model for p̂ is
A. N(0.01877, 0.94)
B. N(0.06, 0.01877)
C. N(0.08, 0.0215)
D. N(0.94, 0.01877)
E. 0.94, 0.0003525)
9. What’s the approximate probability that more than 98% of the 160 seeds in the packet will
germinate?
A. 0.01654
B. 0.98345
C. 0.02990
D. 0.01877
E. 0.92120
QUESTIONS 10 – 13
Statistics from Cornell’s Northeast Regional Climate Center indicate that Ithaca, NY, gets an
average of 35.4 inches of rain each year, with a standard deviation of 4.2 inches.
10. During what percentage of years does Ithaca get more than 42 inches of rain?
A. approximately 84.28%
B. approximately 10.95%
C. approximately 31.2%
D. approximately 5.80%
E. approximately 94.19%
11. Less than how much rain falls in the driest 30% of all years?
A. 70 inches
B. 33.19 inches
C. 64.60 inches
D. 31.9 inches
E. 30 inches
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A Cornell University student is in Ithaca for 8 years. Let y represent the mean amount of rain for
those 8 years.
12. The sampling distribution model of this mean, y , is best described as
A. N(1.484924, 35.4)
B. N(4.2, 35.4)
C. N(35.4, 4.2)
D. N(35.4, 0.828427)
E. N(35.4, 1.484924)
13. What’s the probability that those 8 years average less than 30 inches of rain?
A. 0.8474576
B. 0.0001382
C. 0.9998618
D. 0.2666667
E. 0.7333333
QUESTIONS 14 – 15
Carbon monoxide (CO) emissions for a certain kind of car vary with mean 3.2 g/mi and standard
deviation 0.7 g/mi. A company has 70 of these cars in its fleet. Let y represent the mean CO
level for the company’s fleet.
14. Estimate the probability that y is between 3.3 and 3.4 g/mi.
A. 0.1076
B. 0.8924
C. 0.0836
D. 0.9164
E. 0.9706
15. There is only a 1% chance that the fleet’s mean CO level is greater than what value?
A. 30 gm/mi
B. 0.528 gm/mi
C. 3.39 gm/mi
D. 4.83 gm/mi
E. 1.57 gm/mi
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16. Which of the following is an example of a difference in two proportions based on
independent samples?
A. A random sample of 1000 voters is asked who they plan to vote for in the upcoming
election. The difference is found between the proportion of voters who plan to vote for
the Republican candidate and the proportion of voters who plan to vote for the
Democratic candidate.
B. Each student in a random sample of 500 sophomores and a random sample of 500 seniors
is asked what proportion of classes he or she skips in a typical quarter. The difference in
the average responses for the two groups is found.
C. A random sample of 800 adults in the US in 1999 was asked if they support the
legalization of marijuana, and another random sample of 800 adults was asked the same
question is 2009. The difference in the proportions of adults who supported it in 1999 and
2009 is found.
D. None of the above is an example of a difference in two proportions based on independent
samples.
E. None of the above
17. Which of the following statements is correct about a parameter and a statistic associated
with repeated random samples of the same size from the same population?
A. Values of a parameter will vary from sample to sample but values of a statistic
will not.
B. Values of both a parameter and a statistic may vary from sample to sample.
C. Values of a parameter will vary according to the sampling distribution for that
parameter.
D. Values of a statistic will vary according to the sampling distribution for that
statistic.
E. None of the above
18. Which of the following statements best describes the relationship between a parameter
and a statistic?
A. A parameter has a sampling distribution with the statistic as its mean.
B. A parameter has a sampling distribution that can be used to determine what values the
statistic is likely to have in repeated samples.
C. A parameter is used to estimate a statistic.
D. A statistic is used to estimate a parameter.
E. All of the above
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19. Which one of the following statements is false?
A. The standard error measures the variability of a population parameter.
B. The standard error of a sample statistic measures, roughly, the average difference
between the values of the statistic and the population parameter.
C. Assuming a fixed value of s = sample standard deviation, the standard error of the mean
decreases as the sample size increases.
D. The standard error of a sample proportion decreases as the sample size increases.
E. All of the above
20. For which of the following situations would the Rule for Sample Proportions not apply?
A. A random sample of 100 is taken from a population in which the proportion with the
trait of interest is 0.98.
B. A random sample of 50 is taken from a population in which the proportion with the trait
of interest is 0.50.
C. A binomial experiment is done with n = 500 and p = 0.9.
D. The Rule for Sample Proportions would apply in all of the situations in A, B and C.
E. None of the above
21. The mean of the sampling distribution for a sample proportion depends on the value(s) of
A.
B.
C.
D.
E.
the true population proportion but not the sample size.
the sample size but not the true population proportion.
the sample size and the true population proportion.
neither the sample size nor the true population proportion.
All of the above
22. A television station plans to ask a random sample of 400 city residents if they can name
the news anchor on the evening news at their station. They plan to fire the news anchor if
fewer than 10% of the residents in the sample can do so. Suppose that in fact 12% of city
residents could name the anchor if asked. What is the approximate probability that the
anchor will be fired?
A.
B.
C.
D.
E.
0.02
1.23
0.11
0.89
0.016
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23. Suppose that the mean of the sampling distribution for the difference in two sample
proportions is 0. This tells us that
A.
B.
C.
D.
E.
The two sample proportions are both 0.
The two sample proportions are equal to each other.
The two population proportions are both 0.
The two population proportions are equal to each other.
All of the above
24. For which of the following situations would the Rule for Sample Means not apply?
A.
B.
C.
D.
E.
A random sample of size 20 is drawn from a skewed population.
A random sample of size 50 is drawn from a skewed population.
A random sample of size 20 is drawn from a bell-shaped population.
A random sample of size 50 is drawn from a bell-shaped population.
All of the above
25. Which one of the following statements is false?
A. The sampling distribution of any statistic becomes approximately normal for large
sample sizes.
B. The sampling distribution of the sample mean becomes approximately normal for large
sample sizes.
C. The sampling distribution of the sample mean is exactly normal if the observations are
normally distributed.
D. The standard deviation of the sample mean decreases as the sample size increases.
E. All of the above
26. Suppose that the mean of the sampling distribution for the difference in two sample
means is 0. This tells us that
A.
B.
C.
D.
E.
the two sample means are both 0.
the two sample means are equal to each other.
the two population means are both 0.
the two population means are equal to each other.
None of the above
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Questions 27 – 29
A large car insurance company is conducting a study on behavior behind the wheel to explain the
fact that male drivers (who tend to be thought of as more aggressive drivers) have more
accidents, on average, per year, than female drivers. The average number of accidents per year
for male drivers is 2.3 with a standard deviation of 0.8 and for female drivers the mean is 1.7
with a standard deviation of 0.6. Independent random samples of 25 male and 20 female drivers
are to be selected to take part in the behavior study.
27. If the sample mean number of accidents is to be calculated for both the male and female
drivers and we calculate the difference as male – female, what is the expected value
(mean) for the difference in sample means?
A.
B.
C.
D.
E.
1.7
2.3
0.6
0.8
4.0
28. If the sample mean number of accidents is to be calculated for both the male and female
drivers and we calculate the difference as male – female, what is the standard deviation of
the sampling distribution of the difference in sample means?
A.
B.
C.
D.
E.
0.0436
0.2088
0.2942
0.7
0.14
29. Suppose we can assume that the number of accidents per year is normally distributed,
both for males and for females. What is the probability that the average number of
accidents in the sample of 25 male drivers is less than the average number of accidents in
the sample of 20 female drivers?
A.
B.
C.
D.
E.
0.9980
0.0020
0.0207
0.2266
0.7734
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30. Assume that the duration of human pregnancies can be described by a Normal model
with mean 262 days and standard deviation 13 days. A certain obstetrician is currently
providing prenatal care to 30 pregnant women. Let y represent the mean length of their
pregnancies. What is the probability that the mean duration of these patient’s pregnancies
will be less than 263 days?
A.
B.
C.
D.
E.
0.6628
0.3372
0.5596
0.2817
0.4010
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