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# Chapter 10 Practice MCQ for final exam.doc

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York University

Administrative Studies

ADMS 2320

Marwan Hassan

Winter

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CHAPTER 10
INTRODUCTION TO ESTIMATION
MULTIPLE CHOICE QUESTIONS
In the following multiple-choice questions, please circle the correct answer.
1. The term 1-α refers to:
a. the probability that a confidence interval does not contain the population
parameter
b. the level of confidence
c. the level of unbiasedness
d. the level of consistency
ANSWER: b
2. The letterα in the formula for constructing a confidence interval estimate of
the population mean is
a. the level of confidence
b. the probability that a confidence interval will contain the population mean
c. the probability that a confidence interval will not contain the population
mean
d. the area in the lower tail of the sampling distribution of the sample mean
ANSWER: c
μ
3. A 90% confidence interval estimate of the population mean can be
interpreted to mean that:
a. if we repeatedly draw samples of the same size from the same
population, 90% of the values of the sample means x will result in a
confidence interval that includes the population mean.
b. there is a 90% probability that the population meanμ will lie between
the lower confidence limit (LCL) and the upper confidence limit (UCL).
c. we are 90% confident that we have selected μ sample whose range of
values does not contain the population mean .
d. We are 90% confident that 10% the values of the sample means x will
result in a confidence interval that includes the population me.n
ANSWER: a
4. Which of the following is not a characteristic for a good estimator?
a. Biasedness
160 161 Chapter Ten
b. Consistency
c. Relative efficiency
d. Unbiasedness
ANSWER: a
5. The width of a confidence interval estimate of the population mean widens
when the:
a. level of confidence increases
b. sample size decreases
c. value of the population standard deviation increases
d. All of the above statements are correct
ANSWER: d
6. Which of the following statements is false?
a. The width of a confidence interval estimate of the population mean
narrows when the sample size increases
b. The width of a confidence interval estimate of the population mean
narrows when the value of the sample mean increases
c. The width of a confidence interval estimate of the population mean
widens when the confidence level increases
d. All of the above statements are true
ANSWER: b
7. Which of the following statements is false?
a. The sample size needed to estimate a population mean is directly
proportional to the population variance
b. The sample size needed to estimate a population mean is directly
proportional to the square of the standard normal cutoff value
α / 2
c. The sample size needed to estimate a population mean is directly
proportional to the square of the maximum allowable error W
d. All of the above statements are true
ANSWER: c
μ
8. A 98% confidence interval estimate for a population mean is determined
to be 75.38 to 86.52. If the confidence level is reduced to 90%, the
confidence interval forμ
a. becomes wider
b. remains the same
c. becomes narrower
d. none of the above answers is correct
ANSWER: c
9. The z value for a 96.6% confidence interval estimate is
a. 2.12
b. 1.82 Introduction to Est162tion
c. 2.00
d. 1.96
ANSWER: a
10. In developing an interval estimate for a population mean, the population
standard deviation was assumed to be 10. The interval estimate was 50.92
± 2.14. Had σ equaled 20, the interval estimate would be
a. 60.92 ± 2.14
b. 50.92 ± 12.14
c. 101.84 ± 4.28
d. 50.92 ± 4.28
ANSWER: d
11. In developing an interval estimate for a population mean, a sample of 50
observations was used. The interval estimate was 19.76 1.32. Had the
±
sample size been 200 instead of 50, the interval estimate would have been
a. 19.76 ± .33
b. 19.76 ± .66
c. 9.88 ± 1.32
d. 4.94 ± 1.32
ANSWER: b
12. After constructing a confidence interval estimate for a population mean, you
believe that the interval is useless because it is too wide. In order to correct
this problem, you need to:
a. increase the population standard deviation
b. increase the sample size
c. increase the level of confidence
d. increase the sample mean
ANSWER: b
13. In developing an interval estimate for a population mean, the value of z to
use is
a. 1.15
b. 0.32
c. 1.53
d. 0.16
ANSWER: c
14. The sample size needed to estimate a population mean within 2 units with a
95% confidence when the population standard deviation equals 8 is
a. 9
b. 61
c. 62
d. 8
ANSWER: c
15. A random sample of 64 observations has a mean of 30. The population
variance is assumed to be 9. The 85.3% confidence interval estimate for the
population mean (to the third decimal place) is 163 Chapter Ten
a. 28.369 ± 31.631
b. 29.456 ± 30.544
c. 28.560 ± 31.440
d. 29.383 ± 30.617
ANSWER: b
16. In developing an interval estimate for a population mean, the interval
estimate was 62.84 to 69.46. The population standard deviation was
assumed to be 6.50, and a sample of 100 observations was used. The mean
of the sample was
a. 56.34
b. 62.96
c. 13.24
d. 66.15
ANSWER: d
17. A point estimate is defined as:
a. the average of the sample values
b. the average of the population values
c. a single value that is the best estimate of an unknown population
parameter
d. a single value that is the best estimate of an unknown sample statistic
ANSWER: c
18. An unbiased estimator of a population parameter is defined as:
a. an estimator whose expected value is equal to the parameter
b. an estimator whose variance is equal to one
c. an estimator whose expected value is equal to zero
d. an estimator whose variance goes to zero as the sample size goes to
infinity
ANSWER: a
19. An estimator is said to be consistent if:
a. it is an unbiased estimator
b. the variance of the estimator is close to one
c. the expected value of the estimator is known and positive
d. it is an unbiased estimator and the difference between the estimator and
the population parameter grows smaller as the sample size grows larger
ANSWER: d
20. If there are two unbiased estimators of a population parameter, the one
whose variance is smaller is said to be:
a. a biased estimator
b. relatively efficient
c. consistent
d. relatively unbiased
ANSWER: b
21. Which of the following statements is (are) correct? Introduction to Estim164on
a. The sample mean is an unbiased estimator of the population mean
b. The sample proportion is an unbiased estimator of the population
proportion
c. The difference between two sample means is an unbiased estimator of
the difference between two population means
d. All of the above statements are correct
ANSWER: d
22. Which of the following statements is (are) true?
a. The sample mean is relatively more efficient than the sample median
b. The sample median is relatively more efficient than the sample mean
c. The sample variance is relatively more efficient than the sample variance
d. All of the above statements are true
ANSWER: a
23. The problem with relying on a point estimate of a population parameter is
that:
a. it has no variance
b. it might be unbiased
c. it might not be relatively efficient
d. it does not tell us how close or far the point estimate might be from the
parameter
ANSWER: d
24. A confidence interval is defined as:
a. a point estimate plus or minus a specific level of confidence
b. a lower and upper confidence limit associated with a specific level of
confidence
c. an interval that has a 95% probability of containing the population
parameter
d. a lower and upper confidence limit that has a 95% probability of
containing the population parameter
ANSWER: b
25. As its name suggests, the objective of estimation is to determine the
approximate value of:
a. a population parameter on the basis of a sample statistic
b. a sample statistic on the basis of a population parameter
c. the sample mean
d. the sample variance
ANSWER: a
2
26. The sample variance s is an unbiased estimator of the population variance
σ 2when the denominator of s2 is
a. n + 1
b. n
c. n - 1
d. n - 2
ANSWER: c 165 Chapter Ten
27. Which of the following assumptions must be true in order to use the formula
x ± z σ / n to find a confidence interval estimate of the population mean?
α / 2
a. The population variance is known
b. The population mean is known
c. The population is normally distributed
d. The confidence level is greater than 90%
ANSWER: a
28. In the formula x ± z σ / n, the α / refers to:
α / 2
a. the probability that the confidence interval will contain the population
mean
b. the probability that the confidence interval will not contain the population
mean
c. the area in the lower tail or upper tail of the sampling distribution of the
sample mean
d. the level of confidence
ANSWER: c
29. Which of the following is not a part of the formula for constructing a
confidence interval estimate of the population mean?
a. A point estimate of the population mean
b. The standard error of the sampling distribution of the sample mean
c. The confidence level
d. The value of the population mean
ANSWER: d
30. The larger the level of confidence used in constructing a confidence interval
estimate of the population mean, the:
a. smaller the probability that the confidence interval will contain the
population mean
b. smaller the value of zα / 2
c. wider the confidence interval
d. narrower the confidence interval
ANSWER: c Introduction to Esti166ion
TRUE/FALSE QUESTIONS
31. An interval estimate is a range of values within which the actual value of the
population parameter, such as , may fall.
ANSWER: T
32. A confidence interval is an interval estimate for which there is a specified
degree of certainty that the actual value of the population parameter will fall
within the interval.
ANSWER: T
33. An interval estimate is an estimate of the range for a sample statistic.
ANSWER: F
34. An unbiased estimator of a population parameter is an estimator whose
standard deviation is the same as the actual value of the population standard
deviation.
ANSWER: F
35. The sample proportion is an unbiased estimator of the population proportion,
and that the difference between two sample means is an unbiased estimator
of the difference between two population means.
ANSWER: T
36. The sample standard deviation is an unbiased estimator of the population
standard deviation.
ANSWER: F
37. Knowing that an estimator is unbiased only

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