Transcript lecture7-confidence-intervals-for

Confidence Intervals for
Means
• point estimate – using a single value (or point) to
approximate a population parameter.
– the sample mean is the best point estimate of the population
mean 
• The problem is, with just one point, how do we know how
good that estimate is?
• A confidence interval (or interval estimate) is a range of
interval of values that is likely to contain the true value of
the population parameter.
• confidence interval = estimate  margin of error
• common choices are:
– 90% ( = 0.10);
– 95% ( = 0.05);
– 99% ( = 0.01).
 s 
X  t 2 

 n
 s 
X  t 2 

 n
• When sample sizes are small, we must use the
t-distribution instead of the normal curve (zdistribution). (Appendix C – p477)
• This table relies on ‘degrees of freedom’, which
is always n – 1.
Create a 95% confidence interval for the starting salaries of 20 college
graduates who have taken a statistics course if the mean salary is
$43,704, and the standard deviation is $9879.
 s 
• margin of error t 2  
 n
s = standard deviation = $9879
n = sample size = 20
df= degrees of freedom = n-1=19
tcrit=2.093
 9879 
 s 
2.093
t 2 




20
n




2.093 2209.01  4623.46
 s 
X  t 2 

 n
43704  4623.46  39080.54  x  48327.46