7.3: How Can We Construct a Confidence Interval to Predict a Population Mean
Onesample z Confidence Interval for μ: The general formula for a confidence interval for a population
mean μ when
1.
x
= is the sample mean from a
random sample
.
2.
the
sample size n is lar
ge (generally n ≥ 30), and
3.
σ,
the population standard deviation
, is known is
(
29
x
z critical value
n
σ
±
This interval can also be used if n is small (generally n < 30) but it is reasonable to believe that the
distribution of values in the population is normal.
Filling Machine:
A certain filling machine has a true population standard deviation
σ
= 0.228 ounces
when used to fill catsup bottles.
A random sample of 36 “6 ounce” bottles of catsup was selected from
the output from this machine and the sample mean was 6.018 ounces.
Find a 90% confidence interval
estimate for the true mean fills of catsup from this machine.
Unknown
σ

Small Size Samples [All Size Samples]
t distribution:
If X is a normally distributed random variable, the statistic
/
x
t
s
n
μ

=
follows a t distribution with df = n1
(degrees of freedom).
This statistic
/
x
t
s
n

=
is fairly robust and the results are reasonable for moderate sample sizes (15
and up) if x is just reasonable centrally weighted.
It is also quite reasonable for large sample sizes for
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '07
 Ruffin
 Normal Distribution, Palm, $250, ality, $240, $249

Click to edit the document details