Unit 8

our ______ , E, is equal to a critical value times the standard deviation of the point estimate

margin of error

pi is sometimes expressed as

p

a single value used to approximate a parameter, where the sample proportion p-hat is the best point estimate of the population proportion p( sometimes reported as pi) and the sample mean x-bar is the best point estimate of the population mean u.

point estimate

the standard deviation of the t distribution varies with the ______, but is always greater than 1( unlike the z)

sample size

a normal distribution centered at 0 with a standard deviation larger than 1 that is associated with sample data from a population with an unknown standard deviation.

student's t distribution

there are an infinite number of ______, one for each possible value for degrees of freedom

t distributions

if we select many different samples of size n from the same population and constructed the corresponding confidence intervals, % of them would contain the parameter

theory of a confidence interval

rather, a confidence level of 95% tells us that the process we are using will, in the long run, result in confidence interval limits that contain the true population parameter 95% of the time.

understanding a confidence interval

the t distribution has a mean of ______

0

As the sample size n gets larger, the t distribution get ______ to the z distribution

closer

a range or interval of values used to estimate the true value of a population parameter

confidence interval

confidence interval for estimating a population mean( o unknown) - given either X~N or a large enough sample size to overcome the skewness of X( recall that we default to needing n>= 30 if we know nothing about the skewness), the ____________ is x-bar +/- t(n-1) * (s/squrt(n))

confidence interval

given a simple random sample from a binomial distribution with at least 5 failures and 5 successes

confidence interval for estimating a population proportion

the probability 1 - a( often expressed as a percentage) that, after repeated sampling, the confidence interval contains the parameter of interest, where a is referred to as our significance level

confidence level

a confidence interval is constructed by adding and subtracting a margin of error to our point estimate

constructing a confidence interval

we are __% confident that the interval from __ to __ contains the parameter of interest.

correct interpretation of a confidence interval

the number separating sample statistics that are likely to occur from those that are unlikely, notated with an asterisk, where z*a/2 is a z critical value with the property that it separates an area of a/2 in the right tail of the standard normal distribution.

critical value

the number of sample observations that can vary after certain restrictions have been imposed( for the t distribution, the degrees of freedom are always equal to n-1)

degrees of freedom

t*( critical value) will go up as degree of freedom( df) ______

go down

the t distribution has the same symmetric bell shape as the z distribution, but it reflects the ______ that is expected with estimating o with s

greater variability

there is a __ % probability that the parameter of interest will fall between __ and __

incorrect interpretation of a confidence interval.