Confidence Intervals Flashcards
Estimation
to estimate a population’s parameters using a sample.
Two types of estimates
Point estimate (single number) and interval estimates
Estimator
is a sample statistic used to estimate a population parameter (Xbar used instead of mew)
Two desirable properties for point estimation
1) Expected value of the statistic = parameter (unbiased)
2) small standard deviation for statistic
Better to have a small bias or large sigma?
small bias sometimes better
Confidence Interval
Point Estimate ± margin of error e
Confidence Interval is associated to
a degree of confidence, or confidence level
95% confidence interval means that
We are 95 % confident that interval contains mew
To get a smaller interval, do what?
Either lower level of confidence or increase n.
What if sigma is unknown?
for n≥30, simply replace sigma by s. (assume distribution is close to normal)
What if the sample is small as well (along with unknown sigma)?
We use the t-distribution (Gosset)
how to calculate degrees of freedom for t distribution
df = n-1
t distribution like that of z except what?
Variance of t distribution is always greater than 1.
For df greater than or equal to what is the distribution almost the same as normal?
df≥29
Disadvantages of using t-distribution to calculate confidence intervals
- wider intervals
2. must be able to assume that the underlying distribution is normal.
