Download Topic: Interval Estimate of a Population Mean and a Population

Topic: Interval Estimate of a Population Mean and a Population Proportion
Based on a sample and a given confidence level, an interval estimate can be developed
for a population mean. Here is the formula:
x  t / 2
s
n
Below is the procedure to obtain an interval estimate of a population mean using Excel:
Function>>category ‘Statistical’>>choose the function ‘Confidence’, which returns
the margin error of a confidence interval for a population mean;
Next, specify the value of Alpha () – .01, .05, or 0.1, etc >> enter the value of
Standard deviation >> enter the sample size. The returned value is the margin of error. To
calculate the interval estimate, simply add (subtract) the margin of error to the sample
mean to get the upper (lower) limit of the interval estimates.
Example:
A random sample of 81 checking accounts at a bank showed an average daily
balance of $280. The standard deviation of the population is known to be $66.
a. Is it necessary to know anything about the shape of the population distribution
of the account balances in order to make an interval estimate of the population
mean of the account balances? Explain.
b. Find the standard error of the sample mean.
c. Give a point estimate of the population mean.
d. Construct a 90% confidence interval estimate for the mean.
e. Construct a 95% confidence interval estimate for the mean.
The formula for an interval estimate of a population proportion:
p  z / 2
p 1  p 
,
n
where p is the sample proportion, z / 2 is the z value for a given confidence level, and
n is the sample size. Using embedded functions in Excel, we can calculate the upper and
lower limits of an interval estimate of a population proportion. The example below is
included in the Excel demo for interval estimation:
Response
Yes
No
Yes
Yes
No
Interval Estimate of a Population Proportion
Sample Size
Response of Interest
Count for Response
Sample Proportion
=COUNTA(A2:A901)
Yes
=COUNTIF(A2:A901,D4)
=D5/D3
900
Yes
396
0.44
No
No
Yes
Yes
Yes
No
No
Yes
No
No
Confidence Coefficient 0.95
z Value =NORMSINV(0.5+D8/2)
Standard Error =SQRT(D6*(1-D6)/D3)
Margin of Error =D9*D11
Point Estimate =D5/D3
Lower Limit =D14-D12
Upper Limit =D14+D12
0.95
1.96
0.0165
0.0324
0.44
0.4076
0.4724