Download Page 1 of 2 Chapter 7 Estimates and Sample Sizes 0702

Page 1 of 2
Chapter 7 Estimates and Sample Sizes
0702-SDConfInter.doc – Confidence Intervals and Sample Sizes
This illustrates how to find the Confidence Intervals for a Population
Proportion and for a Population Mean.
Confidence Interval for Proportion:
pˆ  E  p  pˆ  E , where E  z
2
Confidence Interval for Mean:
x  E    x  E , where E  z
pˆ qˆ
n

n
2
or
x  E    x  E , where E  t
s
2
n
NOTE: Remember when to use the z-value and when to use the
t-value.
When entering the confidence level value, the number should be
expressed in a decimal format, such as .95.
Enter a positive whole number for the sample size n.
Enter the number of successes x.
For example, if a survey of 500 people shows that 200 like apple pie,
then n = 500 and x = 200.
(0.0412011, 0.1588989)
(44.00789, 45.99211)
Click on the Evaluate button to obtain the results.
Enter the confidence level as a decimal number.
Enter a positive whole number for the sample size n.
Enter the value of the sample mean.
Enter a positive value of the SAMPLE standard deviation s.
Use the t-value.
Enter a value for the Population Standard Deviation only if it is known
(otherwise, leave it blank). (Entering the value of the SAMPLE
standard deviation in the box for the POPULATION standard deviation
causes the calculations to be based on the normal distribution, and the
results will be affected.)
Click on the Evaluate button to obtain the results.
If the population standard deviation is not known, the confidence
interval will be based on calculations using the t distribution. If the
population standard deviation is known, the confidence interval will be
based on calculations using the normal distribution.
Click on the Print button to print the results.
Use the z-value
(44.02002, 45.97998)
Notice that there is a difference in the two confidence intervals in the
two screens to the left. In the upper screen, the 5 was used as the
SAMPLE standard deviation; thus, the t-value was used. In the lower
screen, the 5 was used as the POPULATION standard deviation; thus,
the z-value was used.
Page 2 of 2
Chapter 7 Estimates and Sample Sizes
0702-SDConfInter.doc – Confidence Intervals and Sample Sizes
Sample Size for Proportion:
2
 z  pˆ qˆ
  2 
When p̂ is known: n 
When p̂ is NOT known,
E2
ˆ  0.5 and qˆ  0.5 in the above formula.
use p
Sample Size for Mean:
 z  
n 2 
 E 
2
When entering the confidence level value, the number should be
expressed in a decimal format, such as .95.
A positive value for the margin of error must be entered as a positive
decimal number less than 1, such as 0.03.
n = 897
Enter a value for "Estimate of p" only if such a value is known
(otherwise, leave it blank). Enter the positive value between 0 and 1
in decimal form. This value might be known from a prior study or
from a reasonable estimate of p.
Enter a value for the population size only if sampling is done without
replacement from a finite population with a known size. (The
population size is usually unknown, and if no entry is made for the
population size, it is assumed that sampling is done with
replacement or the population size is infinite or very large.)
Click on the Evaluate button to obtain the results.
To close the window, click on the X at the top of the module window.
n = 1068
Enter the confidence level value in a decimal format, such as .95.
A positive value for the margin of error must also be entered.
A positive value for the population standard deviation must also be
entered.
n = 385
Enter a value for the population size only if sampling is done without
replacement from a finite population. (The population size is usually
unknown, and if no entry is made for the population size, it is
assumed that sampling is done with replacement or the population
size is infinite or very large.)
Click on the Evaluate button to obtain the results.