Download 0538479825_312312

Chapter 08 Page 1 of 6
WebQuizzing – Ch. 08
Book ISBN-10 0538477490
Book ISBN-13 9780538477499
Author: Gerald Keller
Title: Statistics for Management and Economics
Ed: 9e
# Questions Submitted: 20 Multiple Choice
1. The standard deviation of the sampling distribution of X is also called the:
A. central limit theorem.
B. standard error of the sample mean.
C. finite population correction factor.
D. population standard deviation.
Analysis:
A. Incorrect. The standard deviation of the sampling distribution of X is also called the standard
error of the sample mean.
B. Correct. The standard deviation of the sampling distribution of X is also called the standard
error of the sample mean.
C. Incorrect. The standard deviation of the sampling distribution of X is also called the standard
error of the sample mean.
D. Incorrect. The standard deviation of the sampling distribution of X is also called the standard
error of the sample mean.
ANSWER: B Ref: Section 8.1
2. As a general rule in computing the standard error of the sample mean, the finite population
correction factor is used only if the:
A. sample size is smaller than 5% of the population size.
B. sample size is greater than 5% of the sample size.
C. sample size is more than half of the population size.
D. None of these choices.
Analysis:
A. Incorrect. The correction factor is used only if the sample size is greater than 5% of the
sample size.
B. Correct. The correction factor is used only if the sample size is greater than 5% of the sample
size.
C. Incorrect. The correction factor is used only if the sample size is greater than 5% of the
sample size.
D. Incorrect. The correction factor is used only if the sample size is greater than 5% of the
sample size.
ANSWER: B Ref: Section 8.1
Chapter 08
Page 2 of 6
3. If all possible samples of size n are drawn from an infinite population with a mean of  and
a standard deviation of  , then the standard error of the sample mean is inversely
proportional to:
A. 
B. 
C. n
D. n
Analysis:
A. Incorrect. The standard error of the sample mean is inversely proportional to
B. Incorrect. The standard error of the sample mean is inversely proportional to
C. Incorrect. The standard error of the sample mean is inversely proportional to
D. Correct. The standard error of the sample mean is inversely proportional to
ANSWER: D Ref: Section 8.1
n
n
n
n
4. The finite population correction factor should be used:
A. whenever we are sampling from an infinite population.
B. whenever we are sampling from a finite population.
C. whenever the sample size is large compared to the population size.
D. whenever the sample size is small compared to the population size.
Analysis:
A. Incorrect. The finite population correction factor should be used whenever the sample size is
large compared to the population size.
B. Incorrect. The finite population correction factor should be used whenever the sample size is
large compared to the population size.
C. Correct. The finite population correction factor should be used whenever the sample size is
large compared to the population size.
D. Incorrect. The finite population correction factor should be used whenever the sample size is
large compared to the population size.
ANSWER: C Ref: Section 8.1
5. The Central Limit Theorem states that, if a random sample of size n is drawn from a
population, then the sampling distribution of the sample mean X :
A. is approximately normal if n > 30.
B. is approximately normal if n < 30.
C. is approximately normal if the underlying population is normal.
D. None of these choices.
Chapter 08 Page 3 of 6
Analysis:
A. Correct. The sampling distribution of the sample mean X is approximately normal if n > 30.
B. Incorrect. The sampling distribution of the sample mean X is approximately normal if n >
30.
C. Incorrect. The sampling distribution of the sample mean X is approximately normal if n >
30.
D. Incorrect. The sampling distribution of the sample mean X is approximately normal if n >
30.
ANSWER: A Ref: Section 8.1
6. A sample of size n is selected at random from an infinite population. As n increases, which of
the following statements is true?
A. The population standard deviation decreases.
B. The standard error of the sample mean decreases.
C. The population standard deviation increases.
D. The standard error of the sample mean increases.
Analysis:
A. Incorrect. The standard error of the sample mean decreases is true.
B. Correct. The standard error of the sample mean decreases is true.
C. Incorrect. The standard error of the sample mean decreases is true.
D. Incorrect. The standard error of the sample mean decreases is true.
ANSWER: B Ref: Section 8.1
7. The expected value of the sampling distribution of the sample mean X equals the population
mean  :
A. only when the population is normally distributed.
B. only when the sample size is large.
C. only when the population is infinite.
D. for all populations.
Analysis:
A. Incorrect. The sample mean X equals the population mean  for all populations.
B. Incorrect. The sample mean X equals the population mean  for all populations.
C. Incorrect. The sample mean X equals the population mean  for all populations.
D. Correct. The sample mean X equals the population mean  for all populations.
ANSWER: D Ref: Section 8.1
8. If all possible samples of size n are drawn from a population, the probability distribution of
the sample mean X is called the:
A. standard error of X .
B. expected value of X .
C. sampling distribution of X .
D. normal distribution.
Chapter 08 Page 4 of 6
Analysis:
A. Incorrect. The probability distribution of the sample mean X is called the sampling
distribution of X .
B. Incorrect. The probability distribution of the sample mean X is called the sampling
distribution of X .
C. Correct. The probability distribution of the sample mean X is called the sampling
distribution of X .
D. Incorrect. The probability distribution of the sample mean X is called the sampling
distribution of X .
ANSWER: C Ref: Section 8.1
9. Which of the following is true about the sampling distribution of the sample mean?
A. Its mean is always equal to  n.
B. Its standard error is always equal to the population standard deviation  .
C. Its shape is exactly normal if n is large enough.
D. None of these choices.
Analysis:
A. Incorrect. None of these choices is true.
B. Incorrect. None of these choices is true.
C. Incorrect. None of these choices is true.
D. Correct. None of these choices is true.
ANSWER: D Ref: Section 8.1
10. Which of the following is true regarding the sampling distribution of the mean for a large
sample size? Assume the population distribution is not normal.
A. It has the same shape, mean and standard deviation as the population.
B. It has the same shape and mean as the population, but a different standard deviation.
C. It the same mean and standard deviation as the population, but a different shape.
D. It has the same mean as the population, but a different shape and standard deviation.
Analysis:
A. Incorrect. It has the same mean as the population, but a different shape and standard deviation
is true.
B. Incorrect. It has the same mean as the population, but a different shape and standard deviation
is true.
C. Incorrect. It has the same mean as the population, but a different shape and standard deviation
is true.
D. Correct. It has the same mean as the population, but a different shape and standard deviation
is true.
ANSWER: D Ref: Section 8.1
Chapter 08 Page 5 of 6
11. For a sample size of 1, the sampling distribution of the mean is normally distributed:
A. regardless of the shape of the population.
B. only if the population values are larger than 30.
C. only if the population is normally distributed.
D. None of these choices.
Analysis:
A. Incorrect. The sampling distribution of the mean is normally distributed only if the population
is normally distributed.
B. Incorrect. The sampling distribution of the mean is normally distributed only if the population
is normally distributed.
C. Correct. The sampling distribution of the mean is normally distributed only if the population
is normally distributed.
D. Incorrect. The sampling distribution of the mean is normally distributed only if the population
is normally distributed.
ANSWER: C Ref: Section 8.1
12. Given that X is a binomial random variable with very large n, the binomial probability P(X 
5) is approximated by the area under a normal curve to the right of:
A. 4.5
B. 5.5
C. 4
D. 6
Analysis:
A. Correct. By the area under a normal curve to the right of 4.5
B. Incorrect. By the area under a normal curve to the right of 4.5
C. Incorrect. By the area under a normal curve to the right of 4.5
D. Incorrect. By the area under a normal curve to the right of 4.5
ANSWER: A Ref: Section 8.1
13. As a general rule, the normal distribution is used to approximate the sampling distribution of
the sample proportion only if:
A. the sample size n is greater than 30.
B. the population proportion p is close to 0.50.
C. the underlying population is normal.
D. np and n(1-p) are both greater than or equal to 5.
Analysis:
A. Incorrect. Only if np and n(1-p) are both greater than or equal to 5.
B. Incorrect. Only if np and n(1-p) are both greater than or equal to 5.
C. Incorrect. Only if np and n(1-p) are both greater than or equal to 5.
D. Correct. Only if np and n(1-p) are both greater than or equal to 5.
ANSWER: D Ref: Section 8.1
Chapter 08 Page 6 of 6
14. Given a binomial distribution with n trials and probability p of a success on any trial, a
conventional rule of thumb is that the normal distribution will provide an adequate
approximation of the binomial distribution if:
A. np  5 and n(1-p)  5
B. np  5 and np(1-p)  5
C. np  5 and n(1-p)  5
D. None of these choices.
Analysis:
A. Correct. If np  5 and n(1-p)  5
B. Incorrect If np  5 and n(1-p)  5.
C. Incorrect If np  5 and n(1-p)  5.
D. Incorrect If np  5 and n(1-p)  5.
ANSWER: A Ref: Section 8.1
15. The standard error of the sample proportion gets larger as:
A. p approaches 0
B. p approaches 0.50
C. p approaches 1.00
D. None of these choices.
Analysis:
A. Incorrect. The standard error of the sample proportion gets larger as p approaches 0.50
B. Correct. The standard error of the sample proportion gets larger as p approaches 0.50
C. Incorrect. The standard error of the sample proportion gets larger as p approaches 0.50
D. Incorrect. The standard error of the sample proportion gets larger as p approaches 0.50
ANSWER: B Ref: Section 8.1
16. The standard deviation of P̂ is also called the:
A. standard error of the sample proportion.
B. standard deviation of the population.
C. standard deviation of the binomial.
D. None of these choices.
Analysis:
A. Correct. The standard deviation of P̂ is also called the standard error of the sample
proportion.
B. Incorrect. The standard deviation of P̂ is also called the standard error of the sample
proportion.
C. Incorrect. The standard deviation of P̂ is also called the standard error of the sample
proportion.
D. Incorrect. The standard deviation of P̂ is also called the standard error of the sample
proportion.
ANSWER: A Ref: Section 8.1