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