Transcript Oct 18

Point Estimates
A point estimate is a single number
determined from a sample that is
used to estimate the corresponding
population parameter.
Confidence Intervals
Confidence Interval
Developed from a sample.
Provides a range of likely values for a
parameter.
Expresses the confidence level that the
true population parameter is included.
Confidence Intervals
Lower Confidence
Limit
Upper Confidence
Limit
Point Estimate
95% Confidence Intervals
(Figure 7-3)
0.95
z.025= -1.96
z.025= 1.96
Confidence Interval
- General Format -
Point Estimate  (Critical Value)(Standard Error)
Confidence Intervals
The confidence level refers to a percentage
greater than 50 and less than 100. For a given
size sample it is the percentage that the
interval will contain the true population
value.
Confidence Interval
Estimates
CONFIDENCE INTERVAL
ESTIMATE FOR  ( KNOWN)
xz

n
where:
z = Critical value from standard
normal table
 = Population standard deviation
n = Sample size
Example of a Confidence
Interval Estimate for 
A sample of 100 cans, from a population with
 = 0.20, produced a sample mean equal to
12.09. A 95% confidence interval would be:
xz

n
0.20
12.09  1.96
100
12.09  0.039
12.051 ounces
12.129 ounces
Margin of Error
The margin of error is the largest
possible sampling error at the
specified level of confidence.
Margin of Error
MARGIN OF ERROR (ESTIMATE FOR  WITH
 KNOWN)
ez
where:

n
e = Margin of error
z = Critical value
 = Standard error of the sampling
distribution
n
Example of Impact of Sample
Size on Confidence Intervals
If instead of sample of 100 cans, suppose a sample of 400
cans, from a population with  = 0.20, produced a
sample mean equal to 12.09. A 95% confidence interval
would be:

xz
12.0704 ounces
12.051 ounces
n
0.20
12.09  1.96
400
12.09  0.0196
n=400
n=100
12.1096 ounces
12.129 ounces
Student’s t-Distribution
The t-distribution is a family of distributions:
Bell-shaped and symmetric
Greater area in the tails than the normal.
Defined by its degrees of freedom.
The t-distribution approaches the normal
distribution as the degrees of freedom increase.
Confidence Interval Estimates
CONFIDENCE INTERVAL
( UNKNOWN)
s
x t
n
where:
t = Critical value from t-distribution
with n-1 degrees of freedom
x = Sample mean
s = Sample standard deviation
n = Sample size
Confidence Interval Estimates
CONFIDENCE INTERVAL-LARGE
SAMPLE WITH  UNKNOWN
s
xz
n
where:
z =Value from the standard normal
distribution
x = Sample mean
s = Sample standard deviation
n = Sample size