Chow exam 3
E(Ebar)=
E(X)
margin of error
a value that accounts for the standard error of the estimate and the desired confidence level of the interval
if the population the sample is drawn from is normally distributed, then the sampling distribution of the sample mean is
always normally distributed
the CLT states that as n gets larger, the sampling distribution of the sample proportion
approaches a normal distribution
The CLT is important in statistics because
for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population
what does x bar mean
sample mean
as the sample size increases
standard error of the mean decreases
in hypothesis testing if the null hypothesis is rejected
the alternative hypothesis is true
variance
the average of the squared deviations from the mean
the expected value of x(bar) is equal to
u (greek u)
which of the following is considered an estimate
x(bar)=20
the t distribution
-assumes the population is normally distributed -approaches the normal distribution as a sample size increases -has more area in the tails than does the normal distribution
a 99% confidence interval estimate can be interpreted to mean that
if all possible samples are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval we have 99% confidence that we have selected a sample whose interval does not include the population mean
which of the following is not true about the students t distribution
it is used to construct confidence intervals for the population mean when the population standard deviation is known
what does greek u mean
mean
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 (exact value of P(bar)=p
a population has a mean of 50 and a standard deviation of 10. a random sample of 144 is selected. the expected value of x(bar) is equal to
50 expected value of x(bar)=u
Central Limit Theorem (CLT)
Says that when n is large, the sampling distribution of the sample mean is approximately Normal
expected value
The weighted average of all of the possible outcomes of a probability distribution.
point estimator
a function of the random sample used to make inferences about the value of an unknown population parameter
random variable
a function that assigns numerical values to the outcomes of an experiment
sample statistic
a numerical measure that describes an aspect of a sample
if an economist wishes to determine whether there is evidence that average family income continuously exceeds $25,000
a one-tailed test should be utilized
which of the following is the most accurate
a parameter is a constant even though the value is unknown
simple random sample
a sample of n observations that has the same probability of being selected from the population as any other sample of n oservations
which of the following is true about a sample statistic such as the sample mean or sample proportion
a sample statistic is a random variable
Estimator
a statistic used to estimate a parameter
in a statistical problem, a population consists of
all items of interest
a particular value of an estimator is called
an estimate
supposed a 95% confidence interval for u turns out to be (1,000, 2,100). to make more useful inferences from the data, it is desired to reduce the width of the confidence interval. which of the following will result in a reduced interval width?
both increase the sample size and decrease the confidence interval
the CLT states that, for any distribution, as n gets larger, the sampling distribution of the sample mean becomes
closer to a normal distribution
nonresponse bias
error that results from a systematic difference between those who do and those who do not respond to a measurement instrument
if x is normally distributed with expected value u and standard deviation o, then x(bar) is normally distributed with
expected value u and standard deviation o/root n
the sample size required to approximate the normal distribution depends on
how much the population varies from normality
An assumption made about the value of a population parameter is called a
hypothesis
the variability between sample means is -- the variability between observations
less than
the width of a confidence interval estimate for proportion will be
narrower for 90% confidence than for 95% confidence
Convenience sampling is an example of
nonprobabilistic sampling
general format for confidence interval for u and p
point estimate +/- margin of error
the expected value of p(bar) is the
proportion of success in a populaton
a simple random sample is a sample of observations that is
representative of the population from which it was chosen
the probability distribution of the sample mean is commonly referred to as the
sample distribution of x(bar)
in , the population is divided into strata and then randomly selected observations are taken proportionately from each stratum
stratified random sampling
selection bias
systematic under representation of certain groups from consideration for the sample
the probability of committing a type ! error when the null hypothesis is true is
the level of significance
in hypothesis testing, the tentative assumption about the population parameter is
the null hypothesis
Stratified random sampling is a method of selecting a sample in which
the population is first divided into strata, and then random samples are drawn from each stratum
sampling distribution
the probability distribution of an estimator
confidence interval
the range of values within which a population parameter is estimated to lie
which of these is a characteristic of a "bad" sample
the sample is not representative of the population we are trying to describe
in interval estimation, the t distribution is applicable only when
the sample standard deviation is used to estimate the population standard deviation
which of the following statements about the sampling distribution of the sample mean is incorrect
the standard deviation of the sampling distribution of the sample mean is equal to o(sigma)
bias can occur in sampling. bias refers to
the tendency of a sample statistic to systematically over/under estimate a population 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
if you had access to data that included the entire population, then the value of the parameters would be known and no statistical inference would be required
true
which of the following is an example of a population parameter
u(greek u)
A type 1 error is committed when
we reject a null hypothesis that is true
the standard deviation of the sampling distribution of x(bar) is calculated as
-o/root of n