Chapter 8: Estimating with Confidence
+
Chapter 8: Estimating with Confidence
Section 8.3
Estimating a Population Mean
The One-Sample z Interval for a Population Mean
To calculate a 95% confidence interval for ? , we use the familiar formula:
estimate ¡À (critical value) ? (standard deviation of statistic)
?
20
x ? z *?
? 240.79 ? 1.96?
n
16
? 240.79 ? 9.8
? (230.99,250.59)
One-Sample z Interval for a Population Mean
??
Choose an SRS of size n from a population having unknown mean ? and
known standard deviation ¦Ò. As long as the Normal and Independent
conditions are met, a level C confidence interval for ? is
x ? z*
?
n
The critical value z* is found from the standard Normal distribution.
Estimating a Population Mean
In Section 8.1, we estimated the ¡°mystery mean¡± ? (see page 468) by
constructing a confidence interval using the sample mean = 240.79.
+
?
+ Example ¨C One Sample Z-Interval
for a Population Mean
A bottling machine is operating with a standard
deviation of 0.12 ounce. Suppose that in an SRS of
36 bottles the machine inserted an average of 16.1
ounces into each bottle.
A) Estimate the mean number of ounces in all the
bottles this machine fills
Since ? ? x , then
x ? 16.1
+ Example ¨C One Sample Z-Interval
for a Population Mean
A bottling machine is operating with a standard
deviation of 0.12 ounce. Suppose that in an SRS of
36 bottles the machine inserted an average of 16.1
ounces into each bottle.
B) Give an interval within which we are 95% certain
that the mean lies.
For samples of size 36, the sample means are
approximately normally distributed with a
standard deviation of
?
0.12
?x ?
?
? 0.02
n
36
We want to use
x ? z ?x
*
16.1 ? 1.96 (0.02)
? (16.0608,16.1392)
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- chapter 8 hypothesis testing
- understanding the dependent t test
- finding t critical values with your calculator
- t test nist
- table of critical values for the wilcoxon test
- t critical values colorado state university
- ch9 testing the difference between two means two
- confidence intervals and the t distribution
- table of critical values of t
- 8 3 1 when sigma is known the one sample z interval for a
Related searches
- chapter 8 photosynthesis biology test
- chapter 8 photosynthesis worksheet answ
- chapter 8 photosynthesis
- developmental psychology chapter 8 quizlet
- chapter 8 photosynthesis answer key
- psychology chapter 8 quizlet
- biology chapter 8 photosynthesis answers
- chapter 8 photosynthesis pdf
- chapter 8 psychology quizlet memory
- psychology chapter 8 quizlet learning
- chapter 8 photosynthesis quizlet
- psychology chapter 8 quiz answers