Stats chapter 7

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

what is considered an estimator?

_X_

the probability distribution of the sample mean is commonly referred to as the:

sampling distribution of _x_

Bias can occur in sampling. Bias refers to:

the tendency of a sampling statistic to systematically over- or under-estimate a population parameter

statistic

random variable

in a statistical problem, a population consists of:

all items of interest

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

cannot be determined

the central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sample mean becomes:

closer to a normal distribution

parameter

constant

a particular value of an estimator is called a(n) _____

estimate

the standard deviation of _p_ equals

sq root of p(1-p) / n

we use a calculated sample _______ to make inferences about an unknown population _______

statistic, parameter

selection bias occurs when:

there is a systematic exclusion of certain groups from consideration for the sample

stratified sampling is preferred to cluster sampling when the objective is:

to increase precision

expected value of _x_:

u

the branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter is BEST referred to as _____ _____

inferential statistics

for any population proportion p, the sampling distribution of the sample proportion is approximately normally distributed if:

np is greater than or equal to 5, and n(1-p) is greater than or equal to 5

the expected value of _p_ is the:

proportion of successes in the population

random samples of size 400 are taken from a population whose population proportion is 0.25. the expected value of the sample proportion is:

0.25

a population has a mean of 50 and a standard deviation of 10. A random sample of 256 is selected. the standard deviation of _x_ is equal to:

0.625. standard deviation divided by the square root of the random sample.

central limit theorem

a theorem that allows us to use the normal probability distribution to approximate the sampling distribution of the sample mean whenever the sample size is large

the variance of _x_, which is equal to o2 / n, is:

smaller than the variance of the individual observation o2

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

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

True of false: If we had access to the data that included the entire population, then the values of the parameters would be known and no statistical inference would be required.

True

an example of a sample statistic

_x_

estimate

a particular value of an estimator

example of a simple random sample

a population contains 10 member 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.

example of a stratified random sample

a population contains 10 member 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.

what is a primary requirement for a "good" sample?

it is representative of the population we are trying to describe

which is not a form of bias?

information from the sample is typical of information in the population

stratified random sampling

the population is divided up into mutually exclusive and collectively exhaustive groups called strata. The sample consists of elements from each stratum.

the central limit theorem states that the distribution of the sample mean will be approximately normal if

the sample size is sufficiently large; as a general guideline, n is greater than or equal to 30.