Download Elementary Statistics

Confidence Intervals for a
Population Mean, Standard
Deviation Known
Assumptions
1. Sigma, aka population standard deviation
is known
2. n > 30 (large sample) or population
follows a normal distribution
3. Sample is a simple random sample
(equal chance of being selected)
Definitions
Point estimate = a single value (or point)
used to approximate a population
parameter. Note: sample mean is the best
point estimate of the population mean
Confidence interval = a range or an interval
of values used to estimate the true value
of a population parameter
Definitions
Margin of error = diff. between observed
sample mean and the true value of the
population mean “E” aka “maximum error
of the estimate”
Interpreting a confidence interval
98.08    98.32
We are 95% confident that the interval from
98.08 to 98.32 actually does contain the
true value of the population mean.
TI-83/84 Instructions
TI-83
Finding confidence intervals
1. “Stat” button
2. Choose “Tests” Menu
3. Choose “ZInterval”
4. Highlight “Stats”
5. Enter std dev, mean, n, and C-level
6. “Highlight Calculate” and press “Enter”
Finding Margin of Error : Subtract smallest part of
interval from mean.
Sample Size to Estimate
Population Mean
 z 2 
n

 E 
z
2
= critical z score based on desired
degree of confidence
E = desired margin of error

2
= population standard
deviation
Example 01
Finding critical z score:
Lets find the critical z score for 96% confidence
z / 2
Example 01
Finding critical z score:
Lets find the critical z score for 96% confidence
z / 2
Example 01
Finding critical z score:
z / 2
We are trying to find the z, so looking at it from left to
right, we are interested in 98% or
Example 01
Finding critical z score:
So we find it by using:
INVNORM(.98,0,1) = 2.053748911
z / 2
Range Rule of Thumb: If Sigma
Isn’t Given
HighValue  LowValue

4
Note: When finding the sample size, always
round up if any decimals
Confidence Interval (By Hand)
LB (Lower Bound)  x  z / 2
UB (Upper Bound)  x  z / 2
SE (Standard Error) 

n

n

n