Transcript 8.4 Power Point

Chapter 8: Estimation
Section 4: Choosing the Sample Size
REVIEW

Walter jogs 3 miles and has recorded his
times to run the 3 miles. For the 90 times he
recorded, his mean time is 22.50 minutes
with a standard deviation of 2.40 minutes.
Find a 99% confidence interval.


x  zc 
   x  zc 
n = 90
n
n
x = 22.50
 = 2.40
c = .99
zc = 2.58
2.40
2.40
22.50  (2.58)
   22.50  (2.58)
90
90
22.50  .65    22.50  .65
21.85    23.15
To compute the sample size for
estimating 
2
 zc   

n= 
 E 
Example
A wildlife study is designed to find the mean weight of salmon
caught by an Alaskan fishing company. As a preliminary study, a
random sample of 50 freshly caught salmon is weighed. The
sample standard deviation is 2.15 pounds. How large a sample
should be taken to be 99% confident that the sample mean is
within 0.20 pound of the true mean weight  ?
To compute the sample size for
estimating p
 zc 
pq
 
n=
E
2
To compute sample size when p is not
given
1  zc 
n=  
4 E 
2
Example

The department of public health wants to
estimate the proportion of children who require
corrective lenses for their vision. The health
department wants to be 99% sure that the point
estimate for p will be in error either way by less
than 0.03. How large a sample should the
health department use?

If a preliminary random sample of 100 children
indicates that 23 require corrective lenses, how
large a sample should the health department
use?