ORMS 3310 Module 7
Nonresponse bias occurs when those responding to a survey or poll differ systematically from the nonrespondents.
Answer: TRUE Explanation: Nonresponse bias occurs when those responding to a survey or poll differ systematically from the nonrespondents.
Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. 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
Answer: A Explanation: Since the population is normal, the sampling distribution of the sample mean is normal for any sample size n. The mean and standard error of the sample mean are calculated as = E(X) = μ = $54,000 and se(X) = SD/square root of n = $12,000 / 2 = $6,000. P( > 60,000) = P(Z >1.0) = 1 − P(Z ≤ 1.0) = 1 − 0.8413 = 0.1587. The appropriate Excel function is = 1-NORM.DIST(60000,54000,12000/SQRT(4),TRUE) = 0.1587.
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) 1.8475 B) 3.4133 C) 8.6603 D) 16
Answer: A Explanation: We call standard deviation of the standard error of the sample mean, and it is computed as se(X) = SD/square root of n.
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.
Answer: A Explanation: Averages have less variation than individual observations. Because each sample is likely to contain both high and low observations, the highs and lows cancel one another, making the variation between sample means smaller than the variation between individual observations.
Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. 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
Answer: A Explanation: Since the population is normal, the sampling distribution of sample mean is normal for any sample size n. The standard error of the sample mean is calculated as se(X) = SD/square root of n. = $12,000 / 2 = $6,000.
Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. Using the appropriate normal transformation, 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
Answer: A Explanation: Since the population is normal, the sampling distribution of the sample mean is normal for any sample size n. The mean and standard error of the sample mean are calculated as = E(X) = μ = $54,000 and se(X) = SD/square root of n = $12,000 / 2 = $6,000. P( < 50,000) = P(Z < −0.67) = 0.2514. The appropriate Excel function is =NORMDIST(50000,54000,12000/SQRT(4),TRUE) = 0.2525.
Which of the following meets the requirements of a simple random sample? A) A 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 inclusion in the sample. B) A 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. C) A 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. D) A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include two males chosen at random under the age of 25 and four females chosen at random over 25.
Answer: B Explanation: A simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations.
Which of the following is not a form of bias? A) Portions of the population are excluded or underrepresented from the sample. B) Certain groups in the population are systematically underrepresented in the sample. C) Information from the sample overemphasizes a particular stratum of the population. D) Those responding to a survey or poll differ systematically from the nonrespondents.
Answer: B Explanation: Bias refers to the tendency of sample statistic to systematically over- or underestimate a population parameter.
Selection bias occurs when ________. A) the population has been divided into strata B) portions of the population are underrepresented in the sample C) cluster sampling is used instead of stratified random sampling D) those responding to a survey or poll differ systematically from the nonrespondents
Answer: B Explanation: Selection bias refers to a systematic underrepresentation of certain groups from consideration for a sample.
What is the relationship between the expected value of the sample mean and the population mean? A) E(X) = square root of μ B) E(X) = μ C) E(X) = μ(1 - μ) D) E(X) = μ(1 + σ)
Answer: B Explanation: The expected value of X is the same as the population mean, that is, E(X) = μ.
Which of the following meets the requirements of a cluster sample? A) A population can be divided into 50 city blocks. The sample will include one hundred people who volunteer for the sample from any city block. B) A population can be divided into 50 city blocks. The sample will include one hundred people chosen at random, without regard to the city block where they live. C) A population can be divided into 50 city blocks. The sample will include all residents from two randomly chosen city blocks. D) A population can be divided into 50 city blocks. The sample will include two people chosen at random from each city block.
Answer: C Explanation: A cluster sample includes observations from randomly selected clusters. In this case, two randomly selected clusters from the 50 city blocks will be used to create the sample.
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) proportion
Answer: C Explanation: When a statistic is used to estimate a parameter, it is referred to as an estimator, and a value of the estimator is called an estimate.
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.
Answer: D Explanation: A parameter is a constant, even though its value may be unknown. A statistic, such as the sample mean or the sample proportion, is a random variable whose value depends on the chosen random sample.
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 overestimate or underestimate a population parameter
Answer: D Explanation: Bias refers to the tendency of sample statistic to systematically over- or underestimate a population parameter.
Which of the following meets the requirements of a stratified random sample? A) A 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 inclusion in the sample. B) A 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. C) A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include two males chosen under the age of 25 and four females chosen over the age of 25. D) A 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 the age of 25.
Answer: D Explanation: In stratified random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called strata. Then, the stratified sample includes randomly selected observations from each stratum that are proportional to the stratum's size in the population.
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 nonrespondents
Answer: D Explanation: Nonresponse bias refers to a systematic difference in preferences between respondents and nonrespondents to a survey or a pool.
A parameter is a random variable, whereas a sample statistic is a constant.
Answer: FALSE Explanation: A parameter is a constant, even though its value may be unknown. A sample statistic, such as the sample mean or sample proportion, is a random variable whose value depends on the chosen random sample.
Cluster sampling is preferred over other sampling techniques when the objective is to increase precision.
Answer: FALSE Explanation: Cluster sampling is preferred when the objective is to decrease costs. Stratified sample is preferred when the objective is to increase precision. Accessibility: Keyboard Navigation
For any population X with expected value µ and standard deviation σ, the sampling distribution of X will be approximately normal if the sample size n is sufficiently small. As a general guideline, the normal distribution approximation is justified when n < 30.
Answer: FALSE Explanation: For any population X with expected value µ and standard deviation σ, the sampling distribution of X will be approximately normal if the sample size n is sufficiently large. As a general guideline, the normal distribution approximation is justified when n ≥ 30.
For any sample size n, the sampling distribution of X is normal if the population from which the sample is drawn is uniformly distributed.
Answer: FALSE Explanation: For any sample size n, the sampling distribution of is normal if the population from which the sample is drawn is normally distributed.
If the expected value of a sample mean equals the population mean, the sample mean is biased.
Answer: FALSE Explanation: If the expected value of a sample mean equals the population mean, the sample mean is unbiased.
In cluster random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called clusters. A cluster sample includes randomly selected observations from each cluster, which are proportional to the cluster's size.
Answer: FALSE Explanation: In cluster random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called clusters. A cluster sample includes observations from randomly selected clusters. Instead of taking a subset from each cluster, the entire cluster is selected as part of the sample.
Selection bias occurs when the sample is mistakenly divided into strata, and random samples are drawn from each stratum.
Answer: FALSE Explanation: Selection bias refers to exclusion or underrepresentation of certain groups from consideration for the sample. In other words, selection bias occurs when portions of the population are underrepresented in the sample.
The term point estimator refers to an estimator that provides a single value
Answer: TRUE Explanation: A point estimator provides a single value or a point.
A simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations.
Answer: TRUE Explanation: A simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations. The characteristics of a simple random sample is one of the main reasons that most statistical methods presume simple random sample.
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
Answer: TRUE Explanation: A statistic is used to estimate the corresponding parameter.
Social-desirability bias refers to systematic difference between a group's "socially acceptable" responses to a survey or poll and this group's ultimate choice.
Answer: TRUE Explanation: Social-desirability bias refers to systematic difference between a group's "socially acceptable" responses to a survey or poll and this group's ultimate choice. This is used as one explanation of the polling missteps that occurred in the 2016 election between Donald Trump and Hillary Clinton. Voters might have provided incorrect answers to a survey or poll because they thought that others would look unfavorably on their ultimate choices.
The standard deviation of X (standard error of the sample mean) equals the population standard deviation divided by the square root of the sample size.
Answer: TRUE Explanation: To distinguish the variability between samples from the variability between individual observations, we refer to the standard deviation of the sample mean as to the standard error of the sample mean
Bias refers to the tendency of a sample statistic to systematically overestimate or underestimate a population parameter
Answer: TRUE Explanation: When the information from a sample is not typical of information in the population in a systematic way, we say that bias has occurred.
In stratified random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called strata. Then simple random samples are drawn from each stratum, which are proportional to the stratum's size in the population.
Answer: TRUE Explanation: With stratified random sampling, the population is divided into groups based on one or more classification criteria. Then simple random samples are drawn from each group in sizes proportional to the relative size of each group in the population. These samples are then pooled.
The ________ of the sample mean X is the same as the population mean.
Answer: expected value Explanation: The expected value of X is computed as E(X ) = μ.
Stratified random sampling is preferred when the objective is to ________.
Answer: increase precision Explanation: When the objective of sampling is to increase precision then the stratified random sampling is preferred.
For making statistical inferences, it is essential that the sampling distribution of X is ________ distributed.
Answer: normally Explanation: If the population X from which the sample is drawn is normal, then X is normally distributed.
Cluster sampling is preferred when the objective is to ________.
Answer: reduce costs Explanation: When you need to reduce costs of sampling the cluster sampling is preferred.
What is the relationship between the standard deviation of the sample mean and the population standard deviation?
B) se(X) = SD/square root of n
