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.