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Ch07 - Ch 7 prep questions

Analytical Methods for Business (University of Arizona)

ch07

Student:

1. A population consists of all items of interest in a statistical problem. True False

2. We calculate a parameter to make inferences about a statistic. True False

3. Bias refers to the tendency of a sample statistic to systematically over- or underestimate a population parameter.

True False

4. Selection bias occurs when the sample is mistakenly divided into strata, and random samples are drawn from each stratum.

True False

5. Nonresponse bias occurs when those responding to a survey or poll differ systematically from the non-respondents.

True False

6. A simple random sample is a sample of n observations which has the same probability of being selected from the population as any other sample of n observations.

True False

7. In stratified random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called strata. A stratified sample includes randomly selected observations from each stratum, which are proportional to the stratum's size.

True False

8. A sample consists of all items of interest in a statistical problem, whereas a population is a subset of the population. We calculate a parameter to make inferences about the unknown sample statistic.

True False

9. If we had access to data that encompass the entire population, then the values of the parameters would be known and no statistical inference would be needed.

True False

10. A parameter is a random variable, whereas a sample statistic is a constant. True False

11. When a statistic is used to estimate a parameter, the statistic is referred to as an estimator. A particular value of the estimator is called an estimate.

True False

12. The standard deviation of equals the population standard deviation divided by the square root of the

sample size, or equivalently, .

True False

13. For any sample size n, the sampling distribution of is normal if the population from which the sample is drawn is uniformly distributed.

True False

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14. For any population with expected value µ and standard deviation σ, the sampling distribution of will be approximately normal if the sample size n is sufficiently small. As a general guideline, the

normal distribution approximation is justified when .

True False

15. For any population proportion p, the sampling distribution of will be approximately normal if the

sample size n is sufficiently large. As a general guideline, the normal distribution approximation is

justified when and . True False

16. Which of the following is an example of a sample statistic?

A.

B. µ

C. σ

D. σ2

17. Which of the following is not a population parameter?

A.

B. µ

C. σ

D. σ2

18. A census is an example of .

A. Sample data

B. Sample statistic

C. Population data

D. Population parameter

19. Bias can occur in sampling. Bias refers to .

A. The division of the population into overlapping groups

B. The creation of strata, which are proportional to the stratum's size

C. The use of cluster sampling instead of stratified random sampling

D. The tendency of a sample statistic to systematically over- or underestimate a population parameter

20. Selection bias occurs when .

A. The population has been divided into strata

B. Portions of the population are excluded from the consideration for the sample

C. Cluster sampling is used instead of stratified random sampling

D. Those responding to a survey or poll differ systematically from the non-respondents

21. Nonresponse bias occurs when .

A. The population has been divided into strata

B. Portions of the population are excluded from the sample

C. Cluster sampling is used instead of stratified random sampling

D. Those responding to a survey or poll differ systematically from the non-respondents

22. Which of the following is not a form of bias?

A. Portions of the population are excluded from the sample.

B. Information from the sample is typical of information in the population.

C. Information from the sample overemphasizes a particular stratum of the population.

D. Those responding to a survey or poll differ systematically from the non-respondents.

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23. Which of the following meets the requirements of a simple random sample?

AA population contains 10 members under the age of 25 and 20 members over the age of 25. The sample

. will include six people who volunteer for the sample.

BA population contains 10 members under the age of 25 and 20 members over the age of 25. The sample

. will include six people chosen at random, without regard to age.

CA population contains 10 members under the age of 25 and 20 members over the age of 25. The sample

. will include six males chosen at random, without regard to age.

DA population contains 10 members under the age of 25 and 20 members over the age of 25. The sample

. will include two people chosen at random under the age of 25 and four people chosen at random over 25.

24. Which of the following meets the requirements of a stratified random sample?

AA population contains 10 members under the age of 25 and 20 members over the age of 25. The sample

. will include six people who volunteer for the sample.

BA population contains 10 members under the age of 25 and 20 members over the age of 25. The sample

. will include six people chosen at random, without regard to age.

CA population contains 10 members under the age of 25 and 20 members over the age of 25. The sample

. will include six males chosen at random, without regard to age.

DA population contains 10 members under the age of 25 and 20 members over the age of 25. The sample

. will include two people chosen at random under the age of 25 and four people chosen at random over 25.

25. Which of the following is true about statistics such as the sample mean or sample proportion?

A. A statistic is a constant.

B. A statistic is a parameter.

C. A statistic is always known.

D. A statistic is a random variable.

26. Statistics are used to estimate population parameters, particularly when it is impossible or too expensive

to poll an entire population. A particular value of a statistic is referred to as a(n) .

A. Mean

B. Stratum

C. Estimate

D. Finite correction factor

27. Which of the following is considered an estimator?

A.

B. µ

C. σ

D. σ2

28. Which of the following is considered an estimate?

A.

B.

C.

D.

29. What is the relationship between the expected value of the sample mean and the expected value of the population?

A.

B.

C.

D.

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30. How does the variance of the sample mean compare to the variance of the population?

A. It is smaller and therefore suggests that averages have less variation than individual observations.

B. It is larger and therefore suggests that averages have less variation than individual observations.

C. It is smaller and therefore suggests that averages have more variation than individual observations.

D. It is larger and therefore suggests that averages have more variation than individual observations.

31. What is the relationship between the standard deviation of the sample mean and the population standard deviation?

A.

B.

C.

D.

32. A nursery sells trees of different types and heights. These trees average 60 inches in height with a standard deviation of 16 inches. Suppose that 75 pine trees are sold for planting at City Hall. What is the standard deviation for the sample mean?

A. 1.85

B. 3.41

C. 4

D. 16

33. If a population is known to be normally distributed, what can be said of the sampling distribution of the sample mean drawn from this population?

A. For any sample size n, the sampling distribution of the sample mean is normally distributed.

B. For a sample size , the sampling distribution of the sample mean is normally distributed.

C. For a sample size , the sampling distribution of the sample mean is normally distributed.

D. For a sample size , the sampling distribution of the sample mean is normally distributed.

34. Over the entire six years that students attend an Ohio elementary school, they are absent, on average,

28 days due to influenza. Assume that the standard deviation over this time period is days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza.

Refer to Exhibit 7-1. What is the expected value for the sampling distribution of the number of school days missed due to influenza?

A. 6

B. 9

C. 28

D. 168

35. Over the entire six years that students attend an Ohio elementary school, they are absent, on average,

28 days due to influenza. Assume that the standard deviation over this time period is days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza.

Refer to Exhibit 7-1. What is the standard deviation for the sampling distribution of the number of school days missed due to influenza?

A. 1.22

B. 1.50

C. 2.25

D. 9.00

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36. Over the entire six years that students attend an Ohio elementary school, they are absent, on average,

28 days due to influenza. Assume that the standard deviation over this time period is days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza.

Refer to Exhibit 7-1. The probability that the sample mean is less than 30 school days is .

A. 0.0918

B. 0.4129

C. 0.5871

D. 0.9082

37. Over the entire six years that students attend an Ohio elementary school, they are absent, on average,

28 days due to influenza. Assume that the standard deviation over this time period is days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza.

Refer to Exhibit 7-1. The probability that the sample mean is between 25 and 30 school days is

.

A. 0.0228

B. 0.0918

C. 0.8854

D. 0.9082

38. Suppose that, on average, electricians earn approximately dollars per year in the United

States. Assume that the distribution for electrician's yearly earnings is normally distributed and that the

standard deviation is dollars.

Refer to Exhibit 7-2. Given a sample of four electricians, what is the standard deviation for the sampling distribution of the sample mean?

A. 6,000

B. 12,000

C. 36,000

D. 54,000

39. Suppose that, on average, electricians earn approximately dollars per year in the United

States. Assume that the distribution for electrician's yearly earnings is normally distributed and that the

standard deviation is dollars.

Refer to Exhibit 7-2. What is the probability that the average salary of four randomly selected electricians exceeds \$60,000?

A. 0.1587

B. 0.3085

C. 0.6915

D. 0.8413

40. Suppose that, on average, electricians earn approximately dollars per year in the United

States. Assume that the distribution for electrician's yearly earnings is normally distributed and that the

standard deviation is dollars.

Refer to Exhibit 7-2. What is the probability that the average salary of four randomly selected electricians is less than \$50,000?

A. 0.2514

B. 0.3707

C. 0.6293

D. 0.7486

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41. Suppose that, on average, electricians earn approximately dollars per year in the United

States. Assume that the distribution for electrician's yearly earnings is normally distributed and that the

standard deviation is dollars.

Refer to Exhibit 7-2. What is the probability that the average salary of four randomly selected electricians is more than \$50,000 but less than \$60,000?

A. 0.5899

B. 0.7486

C. 0.8413

D. 0.9048

42. Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13.

Refer to Exhibit 7-3. What is the probability that in a one-game playoff, her score is more than 227?

A. 0.2676

B. 0.4404

C. 0.5596

D. 0.7324

43. Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13.

Refer to Exhibit 7-3. If during a typical week Susan bowls 16 games, what is the probability that her average score is more than 230?

A. 0.0618

B. 0.3520

C. 0.6480

D. 0.9382

44. Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13.

Refer to Exhibit 7-3. If during a typical week Susan bowls 16 games, what is the probability that her average score for the week is between 220 and 228?

A. 0.0618

B. 0.2390

C. 0.7594

D. 0.8212

45. Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13.

Refer to Exhibit 7-3. If during a typical month Susan bowls 64 games, what is the probability that her average score in this month is above 227?

A. 0.1093

B. 0.4404

C. 0.5596

D. 0.8907

46. Professor Elderman has given the same multiple choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12.

Refer to Exhibit 7-4. What is the probability that a class of 15 students will have a class average greater than 70 on Professor Elderman's final exam?

A. 0.0262

B. 0.6915

C. 0.9738

D. Cannot be determined.

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47. Professor Elderman has given the same multiple choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12.

Refer to Exhibit 7-4. What is the probability that a class of 36 students will have an average greater than

70 on Professor Elderman's final exam?

A. 0.0014

B. 0.3085

C. 0.6915

D. 0.9986

48. Professor Elderman has given the same multiple choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12.

Refer to Exhibit 7-4. Professor Elderman offers his class of 36 a pizza party if the class average is above

80. What is the probability that he will have to deliver on his promise?

A. 0.0228

B. 0.3707

C. 0.6293

D. 0.9772

49. Professor Elderman has given the same multiple choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12.

Refer to Exhibit 7-4. What is the probability Professor Elderman's class of 36 has a class average below 78?

A. 0.1587

B. 0.5675

C. 0.8413

D. Cannot be determined.

50. According to the central limit theorem, the distribution of the sample means is normal if

.

A. The underlying population is normal

B. The sample size

C. If the standard deviation of the population is known

D. Both A and B are correct

51. The central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the

sample mean .

A. Becomes larger

B. Becomes smaller

C. Is closer to a normal distribution

D. Is closer to the standard deviation

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52. A random sample of size 36 is taken from a population with mean and standard deviation

.

Refer to Exhibit 7-5. What is the expected value and the standard deviation for the sampling distribution of the sample mean?

A. Option A

B. Option B

C. Option C

D. Option D

53. A random sample of size 36 is taken from a population with mean and standard deviation

.

Refer to Exhibit 7-5. The probability that the sample mean is greater than 18 is .

A. 0.1587

B. 0.4325

C. 0.5675

D. 0.8413

54. A random sample of size 36 is taken from a population with mean and standard deviation

.

Refer to Exhibit 7-5. The probability that the sample mean is less than 15 is .

A. 0.0228

B. 0.3707

C. 0.6293

D. 0.9772

55. A random sample of size 36 is taken from a population with mean and standard deviation

.

Refer to Exhibit 7-5. The probability that the sample mean is between 15 and 18 is .

A. 0.0228

B. 0.8185

C. 0.8413

D. 0.8641

56. Using the central limit theorem, applied to the sampling distribution of the sample proportion, what conditions must be met?

A.

B.

C.

D.

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57. A random sample of size 100 is taken from a population described by the proportion .

Refer to Exhibit 7-6. What is the expected value and the standard deviation for the sampling distribution of the sample proportion?

A. Option A

B. Option B

C. Option C

D. Option D

58. A random sample of size 100 is taken from a population described by the proportion .

Refer to Exhibit 7-6. The probability that the sample proportion is greater than 0.62 is .

A. 0.3409

B. 0.4082

C. 0.6591

D.

59. A random sample of size 100 is taken from a population described by the proportion .

Refer to Exhibit 7-6. The probability that the sample proportion is less than 0.55 is .

A.

B. 0.1539

C. 0.3669

D. 0.8461

60. A random sample of size 100 is taken from a population described by the proportion .

Refer to Exhibit 7-6. The probability that the sample proportion is between 0.55 and 0.62 is .

A. 0.1539

B. 0.5052

C. 0.6591

D. 0.8130

61. A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students.

Refer to Exhibit 7-7. What are the expected value and the standard deviation for the proportion of students that receive an A?

A. Option A

B. Option B

C. Option C

D. Option D

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