Chapter 8: Estimation
Section 2: Estimating  with Small
Samples
Student’s T Distribution
degrees of freedom df = n – 1
population of x values must be
normal or approximately normal
resembles the standard normal curve
– total area under curve = 1
– centered at 0
– symmetric about 0
– more spread out than the standard
normal curve
as n gets large, df gets large, curve
gets closer to the standard normal
curve
Confidence Interval
s
s
x  tc 
   x  tc 
n
n
Example
A company has a new process
for manufacturing large artificial
sapphires. In a trial run, 12
sapphires are produced. The
mean weight for these 12 gems
is 6.75 carats, with a standard
deviation of 0.33 carat. Find a
95% confidence interval for the
population mean.