Interval
estimation
involves using sample data to determine a range (interval) that, at an established level
of confidence, that is expected to contain the mean of the population.
Steps
1. Determine confidence level (df=n1; alpha
.05, 2tailed)
2. Use either z distribution (if n>120) or t
distribution (for all sizes of n).
3. Use the appropriate table to find the critical
value for a 2tailed test
4. Multiple hypotheses can be compared with the
estimated interval for the population to determine their significance. In other words,
differing values of population means can be compared with the interval estimation to
determine if the hypothesized population means fall within the region of rejection.
Estimation
Formula
where
= sample mean
CV
= critical value (consult distribution table for df=n1 and chosen alpha
commonly .05)
= Standard error of the mean
Note: assumes
sample standard deviation was calculated using:
Example:
Interval Estimation for Means
Problem:
A random sample of 30 incoming college freshmen revealed the following statistics: mean
age 19.5 years; sample standard deviation 1.2. Based on a 5% chance of error, estimate the
range of possible mean ages for all incoming college freshmen.
Estimation
Critical
value
(CV)
Df=n1
or 29
Consult
tdistribution
for alpha
.05, 2tailed
CV=2.045
Standard
error
Estimate
Interpretation
We
are 95% confident that the actual mean age of the all incoming freshmen will be somewhere
between 19 years (the lower limit) and 20 years (the upper limit) of age.
Software Output Example
