Estimating with Uncertainty Flashcards
estimation
process of inferring a population parameter from sample data
how does the estimation of a parameter reflect the population parameter
almost NEVER the exact same as the value of the population parameter being estimated
what do we want to know about the estimate of a sample
how precise it is (how close to the true value in the population it is)
sampling distribution
probability distribution of all the values for an estimate that we MIGHT have obtained when sampled the population
what is the sampling distribution used to determine
how precise the estimate is
what does sampling distribution represent
the “population” of values for an estimate
how does the spread of sampling distribution depend on sample size
Larger the sample size = the narrower the sampling distribution = the more precise the estimate
standard error reflects
differences between an estimate and the target parameter = reflects the precision of an estimate
smaller vs larger standard error
smaller = more precise estimate
larger error = less precise estimate
what is the relationship between standard error and sample size
as sample size INCREASES the standard error DECREASES
Confidence intervals is used because it
Quantifies uncertainty about the value of a parameter
what are confidence intervals
Range of numbers surrounding the sample estimate that is likely to contain the unknown value of the population parameter
what is the 95% confidence interval for the mean
A range likely to contain the value of the true population mean which extends above and below the sample mean
what do the numbers between the upper and lower bounds for a confidence interval represent
most plausible values for the parameter
Values OUTSIDE the confidence interval are
less plausible for the true value of the parameter in the population
Width of the 95% confidence interval
measure of uncertainty about the true value of the parameter
broad vs narrow confidence interval width
broad = uncertainty is high = data not informative about location of population parameter
narrow = uncertainty is low = data is informative about the location of population parameter
how is the approximate of the 95% confidence interval for mean population calculated
adding (upper limit) or subtracting (lower limit) two standard errors from the sample mean
Error bars
Lines on a graph extending outward from the sample estimate that illustrates precision of an estimate
Y bar is the estimate of
mu (population mean)
s is the estimate of
sigma (population standard deviation
P hat is the estimate of
p the population proportion
what must be known for estimates to be useful
the precision of said estimates
what is the process of estimation
the process of inferring a population parameter from sample data
are estimates often the same as the population parameters
NO - chance events make samples different from the true pop parameter
sampling distribution of the estimate
probability distribution of ALL values for an estimate we MIGHT have obtained when sampling the population REPEATEDLY
sampling distribution of sample mean
sampling distribution = the probability distribution of values (for mean) that we MIGHT of obtained when sampling population repeatedly
what is key in regards to the sample mean distribution
the true value of the population (mu) is a CONSTANT - has one distinct value while the sample mean is a VARIABLE - changes with every sample distribution taken
when is the y bar sample unbiased
when it corresponds to mu (represents the exact value of the pop parameter)
how does sample size affect sampling distribution of mean
larger sample = narrower sample distribution = more precise the population estimate
standard error
for an estimate its the standard deviation of the estimate’s sampling distribution
are large or small standard errors more precise
small errors = smaller standard deviation of data = values are tightly clustered around the true value
how to calculate Standard error of the sample mean (SEM)
SAMPLE standard deviation of variable Y divided by the sample size
confidence interval
range of values that surround a sample estimate that is LIKELY to contain the population parameter (but NOT ALWAYS)
95% confidence interval of the mean
range, extending above and beyond the sample mean, likely to contain the mean population parameter (mu)
can all numbers in the 95% C.L be plausible for the true value
YES - 95% CI does not give the EXACT value but a range that it COULD be in
are narrower or wider CI’s more informative
narrower = more information for pop true value
error bars
lines that extend from sample estimates that give information about the precision of the estimate
