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).

• When sample sizes are small, we must use the t-distribution instead of the normal curve (z-distribution). (Appendix C – p477)

• This table relies on ‘degrees of freedom’, which is always n – 1.

2

sX t

n

2

sX t

n

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.

• margin of error

s = standard deviation = $9879

n = sample size = 20

df= degrees of freedom = n-1=19

tcrit=2.093

2

st

n

2

st

n

2.093 2209.01 9879

2.09320

4623.46

2

sX t

n

43704 4623.46 39080.54 48327.46x