stats chapter 7

statistic

random variable

a simple random sample is a sample of observations that is

representative of the population from which it was chosen

standard deviation of p- equals

square root p(1-p)/n

if X is normally distributed with expected value u and SD ó, then x- is normally distributed with

expected value u and SD ó/square root n

in _____, the population is divided up into strata and then randomly selected observations and taken proportionately from each stratum

stratified random sampling

T/F: if we had access to data that included the entire population, then the values of the parameters would be known an no statistical inference would be required

true

cluster sampling works best

when most of the variation of a population is within groups and not between groups

a particular value of an estimator is called an

estimate

when a sample statistic is used to make inferences about a population parameter, it is referred to as an

estimator

the sample size required to approximate the normal distribution depends on

how much the population varies from normality

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

increase precision

branch of stats that uses statistics to estimate a population parameter or test a hypothesis about such a parameter is best referred to as

inferential statistics

the further a population deviates from p=0.50, the ___ sample size required in order to satisfy a normal approximation

larger

in general, the variability between sample means is ___ the variability between observations

less than

population consists of all items of interest in a statistical problem, whereas a ___ is a subset of a pop

sample

the variance of x, which is equal to ó^2/n, is

smaller than the variance of the individual observation ó^2

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>= 30

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

x-

which is most accurate

a parameter is a constant although its value may be unknown

a pop has a mean of 50 and a SD of 10. A random sample of 144 is selected. The expected value of x is equal to

50

which is true about a sample statistics such as the sample mean or sample proportion

a sample statistic is a random variable

selection bias occurs when

portions of the population are excluded from the consideration for the sample

the expected value of p- is the

proportion successes in the population

parameter

constant

if p- is the value that a normal random variable assumes, then we can transform it into its standard normal value as

(p- - p)/ square root p(1-p)/n

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

0.25

a population has a mean of 50 and a SD of 10. A random sample of 256 is selected. The SD of x- is equal to

0.625

if a sample statistic consistently over or under estimates a population parameter, then there is ____

bias

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

a population has a mean of 100 and a SD of 10. A random sample of 25 is selected. The expected value of x- is equal to

100

a population has a mean of 100 and a SD of 12. A random sample of 36 is selected. The SD of x is equal to

2

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

central limit theorem

if the population from which the sample is drawn is normally distributed, then the sampling distribution of the sample mean is

always normally distributed