Download Exam 3 Spring 12 - NCSU Statistics

BUS/ST 350
Exam 3
Spring 2012
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1
VERSION 1 BUS/ST 350 Spring 2012 Exam 3 VERSION 1
Insurance company records indicate that 10% of its policyholders file claims involving theft or robbery of personal property
from their homes. Suppose a random sample of 400 policyholders is selected.
1) The probability that the sample proportion of policyholders filing claims involving theft or robbery from their
homes is less than 8% is
A) 0.7892
B) 0.0517
C) 0.4082
D) 0.0918
E) 0.1333
2) The width of a confidence interval estimate for a proportion will be
A) wider for a sample size of 100 than for a sample size of 50.
B) narrower when the sample proportion is 0.50 than when the sample proportion is 0.20.
C) narrower for 90% confidence than for 95% confidence.
D) narrower for 99% confidence than for 95% confidence.
3) What type of car is more popular among college students, American or foreign? One hundred fifty-nine
college students were randomly sampled and each was asked which type of car he or she prefers.. The
resulting 90% confidence interval for the proportion p of college students that prefer American cars is (0.332,
0.460). Which of the following is a correct interpretation of the interval?
A) 90% of all college students prefer American cars between .332 and .460 of the time.
B) We are 90% confident that the proportion p of all college students who prefer American cars falls between
.332 and .460.
C) We are 90% confident that the interval (0.332, 0.460) contains the true proportion p of all college students
who prefer American cars.
D) We are 90% confident that the sample proportion of the 159 sampled students who prefer American cars
falls between .332 and .460.
E) Between 0.332 and 0.446 of American cars are preferred by college students.
4) In one region of the country, the distribution of September energy consumption for single-family homes can be
described by a normal model with mean 1050 kWh and standard deviation 218 kWh. Find the 33rd percentile
of the consumption level, that is, find the consumption level separating the bottom 33% from the top 67%.
A) 1141.6
B) 969.3
C) 978.1
D) 954.1
5) The owner of a computer repair shop has determined that their daily revenue has mean $7200 and standard
deviation $1200. The daily revenue totals for the next 30 days will be monitored. What is the probability that
the mean daily revenue for the next 30 days will exceed $7500?
A) 0.0869
B) 0.0853
C) 0.9131
D) 0.9147
6) In a college student poll, it is of interest to estimate the proportion p of students in favor of changing from a
quarter-system to a semester-system. How many students should be polled so that we can estimate p to
within 0.09 using a 99% confidence interval? No information is available concerning an approximate value of
p.
A) 114
B) 182
C) 261
D) 206
7) A university dean is interested in determining the proportion of students who receive some sort of financial
aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118
of them are receiving financial aid. Use a 99% confidence interval to estimate the true proportion of students on
financial aid.
A) 0.59 ± 0.623
B) 0.59 ± 0.090
C) 0.59 ± 0.007
D) 0.59 ± 0.003
VERSION 1 BUS/ST 350 Spring 2012 Exam 3 VERSION 1
VERSION 1 BUS/ST 350 Spring 2012 Exam 3 VERSION 1
8) Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If
P(0 < z < k) = 0.4608, find the value of k.
A) 0.61
B) 0.1772
C) 1.76
D) -0.10
Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard
deviation 1.
9)
A) 0.4656
B) -0.0344
C) 0.9656
D) 0.0344
10) Five years ago at a large university the proportion of business major that were female was 0.54. Using the
information above, what total size sample would be necessary if we wanted to estimate the current true
proportion to within ±0.08 using 95% confidence?
A) 105
B) 597
C) 420
D) 150
11) In New York City 36% of adults in the city have credit card debts of more than $2000. A simple random
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sample of n = 100 adults is obtained from New York City. Describe the sampling distribution of p, the sample
proportion of adults who have credit card debts of more than $2000.
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A) Approximately normal; E(p) = 36, SD(p) = 4.8
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B) Approximately normal; E(p) = 0.36, SD(p) = 0.048
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C) Binomial; E(p) = 36, SD(p) = 4.80
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D) Approximately normal; E(p) = 0.36, SD(p) = 0.0023
12) We have calculated a confidence interval based on a sample of size n = 100. Now we want a new interval with
the same level of condfidence but with a margin of error that is only one-fourth as large. How large does our
new sample need to be?
A) 200
B) 25
C) 400
D) 50
E) 1600
13) The manager at a local movie theater has collected data for a long period of time and has concluded that the
distribution of revenue from concession sales during the first show each evening can be described by a normal
model with mean $333.60 and standard deviation $80. Based on this information, what is the probability that
the revenue on the first show will be between $300 and $500?
A) 0.6400
B) 0.6602
C) 0.3184
D) 0.6440
14) A P-value indicates
A) the probability that the null hypothesis is true.
B) the probability of obtaining a value of the test statistic as extreme or more extreme than what we
obtained, given that the alternative hypothesis is true
C) the probability that the alternative hypothesis is true.
D) the probability of obtaining a value of the test statistic as extreme or more extreme than what we
obtained, given that the null hypothesis is true.
E) The probability that we have made a mistake.
VERSION 1 BUS/ST 350 Spring 2012 Exam 3 VERSION 1
VERSION 1 BUS/ST 350 Spring 2012 Exam 3 VERSION 1
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
15) Shaded area is 0.0694.
A) 1.26
B) 1.39
C) 1.48
D) 1.45
16) The distribution of the volume of soda in quart soda bottles can be described by a normal model with mean
32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly
selected bottle will be less than 32 oz?
A) 0.0987
B) 0.4013
C) 0.5987
D) 0.3821
17) A medical school claims that more than 28% of its students plan to go into general practice. It is found that
among a random sample of 130 of the school's students, 32.3% of them plan to go into general practice. The
approximate P-value for the test H0: p = 0.28, Ha: p > 0.28 of the school's claim is
A) 0.3078
B) 0.1370
C) 0.1469
D) 0.8630
18) A truck company wants on-time delivery for 98% of the parts they order from a metal manufacturing plant.
They have been ordering from Hudson Manufacturing but will switch to a new, cheaper manufacturer
(Steel-R-Us) unless there is evidence that this new manufacturer cannot meet the 98% on-time goal. As a
test the truck company purchases a random sample of metal parts from Steel-R-Us, and then determines if
these parts were delivered on-time. Which hypotheses should they test?
A) H0 : p = 0.98
HA: p > 0.98
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B) H0 : p = 0.98
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HA: p < 0.98
C) H0 : p = 0.98
HA: p < 0.98
D) H0 : p > 0.98
HA: p = 0.9
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E) H0 : p = 0.98
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HA: p > 0.98
VERSION 1 BUS/ST 350 Spring 2012 Exam 3 VERSION 1
ANSWERS:
1. D 2. C 3. C 4. D 5. B 6. D 7. B 8. C 9. C 10. D 11. B 12. E 13. D 14. D
15. C 16. B 17. B 18. C