Download quiz 5 solutions

STT 315 Lecture 3
03/13/2014
Quiz 5 (Chapter 5)
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Directions: The quiz contains 8 multiple choice questions. Each question will be worth 2 points so that total points for this quiz is 16.
There is only one correct answer per question. If you would like to get partial credit, show your work below the question where it is
appropriate. The formulas which may be needed for the quiz are given below.
1) The probability distribution shown below describes a population of measurements.
1)
x
0
2
4
p(x) 1/3 1/3 1/3
Suppose that we took repeated random samples of n = 2 observations from the population
described above. Which of the following would represent the sampling distribution of the sample
mean?
x
A)
0
1
2
3
4
B)
p(x) 2/9 2/9 1/9 2/9 2/9
x
C)
0
1
2
3
x
0
2
4
p(x) 1/3 1/3 1/3
4
D)
p(x) 1/9 2/9 3/9 2/9 1/9
x
0
1
2
3
4
p(x) 1/5 1/5 1/5 1/5 1/5
Work:
2) The sampling distribution of the sample mean is shown below.
x
4
5
6
7
2)
8
p(x) 1/9 2/9 3/9 2/9 1/9
Find the expected value of the sampling distribution of the sample mean.
A) 7
B) 4
C) 6
Work:
1
D) 5
3) The number of cars running a red light in a day, at a given intersection, possesses a distribution
with a mean of 1.7 cars and a standard deviation of 5. The number of cars running the red light was
observed on 100 randomly chosen days and the mean number of cars calculated. Describe the
sampling distribution of the sample mean.
A) approximately normal with mean = 1.7 and standard deviation = 5
B) approximately normal with mean = 1.7 and standard deviation = 0.5
C) shape unknown with mean = 1.7 and standard deviation = 5
D) shape unknown with mean = 1.7 and standard deviation = 0.5
3)
Work:
4) The average score of all golfers for a particular course has a mean of 66 and a standard deviation of
3.5. Suppose 49 golfers played the course today. Find the probability that the average score of the
49 golfers exceeded 67.
A) .3707
B) .1293
C) .4772
D) .0228
4)
Work:
5) Suppose a random sample of n measurements is selected from a binomial population with
probability of success p = .32. Given n = 400, describe the shape, and find the mean and the
5)
^
standard deviation of the sampling distribution of the sample proportion, p.
A) approximately normal; 0.32, 0.023
B) approximately normal; 0.32, 0.0005
C) skewed right; 0.32, 0.023
D) skewed right; 128, 9.33
Work:
6) It is generally belived that electrical problems affect about 14% of new cars. An automobile
mechanic conducts diagnostic tests on 128 new cars on the lot. Find the probability that in this
group over 18% of the new cars will be found to have electrical problems.
A) 0.4032
B) 0.0961
C) 0.379
D) 0.121
6)
Work:
7) Which of the following statements is false?
A) A statistic is unbiased if the mean of the sampling distribution is equal to the parameter it is
intended to estimate.
B) Sample statistics are random variables, because different samples can lead to different values
of the sample statistics.
C) The ideal estimator has the greatest variance among all unbiased estimators.
D) The sampling distribution of a sample statistic calculated from a sample of n measurements is
the probability distribution of the statistic.
7)
8) The Central Limit Theorem is considered powerful in statistics because __________.
A) it works for any sample size provided the population is normal
B) it works for any sample provided the population distribution is known
C) it works for any population distribution provided the population mean is known
D) it works for any population distribution provided the sample size is sufficiently large
8)
2
Answer Key
Testname: STT315_QUIZ 5_A_SOLUTIONS
1)
2)
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8)
C
C
B
D
A
B
C
D
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