QM 235 Chapter7

Which of the following is not a form of bias?

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

John would like to conduct a survey in his neighborhood to get homeowners' opinions on the Delmarva proposal to switch to natural gas. Which of the following is an example of a stratified sample?

John randomly chooses three streets and selects every third house on those streets.

Stratified random sampling is preferred when the objective is to _______.

increase precision

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

True

Which of the following is considered an estimate?

X bar = 12

Cluster sampling is preferred when the objective is to _______.

reduce costs

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

se (X)= standard deviation/ square root of n

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

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.

Which of the following is considered an estimator?

X or X bar

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

A statistic is a random variable.

Bias can occur in sampling. Bias refers to _______.

the tendency of a sample statistic to systematically over- or underestimate a population parameter

Nonresponse bias occurs when _______.

those responding to a survey or poll differ systematically from the nonrespondents

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.

true

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

the sample size n ≥ 30

A point estimator refers to an estimator that provides a single value.

true

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

Nonresponse bias occurs when those responding to a survey or poll differ systematically from the nonrespondents.

true

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) _______.

estimate

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

false

For making statistical inferences, it is essential that the sampling distribution of X is _________ distributed.

normally

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

E(X)= u

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?

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

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

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

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.

false: 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.

false: For any sample size n, the sampling distribution of X 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.

false: If the expected value of a sample mean equals the population mean, the sample mean is unbiased.

The central limit theorem approximation improves as the sample size decreases.

false: The central limit theorem approximation improves as the sample size increases.

The standard deviation of X suggests that the variation between observations is smaller than the variation between averages.

false: The standard deviation of the sample mean (standard error of the sample mean) suggests the variation between averages is less than the variation between observations.

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

is closer to a normal distribution