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