7.4. Confidence Intervals http://www.ck12.org
Example:
Julianne collects four samples of size 60 from a known population with a population standard deviation of 19 and a
population mean of 110. Using the four samples, she calculates the four sample means to be:
107 112 109 115
a) For each sample, determine the 90% confidence interval?
b) Do all four confidence intervals enclose the population mean? Explain.
Solution:
a)
x ̄±z
σ
√
nx ̄±z
σ
√
nx ̄±z
σ
√
n
107 ± 1. 64519
√
60
112 ± 1. 645
19
√
60
109 ± 1. 645
19
√
60
107 ± 4. 04 112 ± 4. 04 109 ± 4. 04
from 102.96 to 111. 04 from 107.96 to 116. 04 from 104.96 to 113. 04x ̄±zσ
√
n
115 ± 1. 64519
√
60
115 ± 4. 04
from 110.96 to 119. 04b) Three of the confidence intervals enclose the population mean. The interval from 110.96 to 119.04 do not enclose
the population mean.
Example:
Now it is time to use the graphing calculator to simulate the collection of three samples of different sizes− 30 , 60 , 90
respectively. The three sample means will be calculated as well as the three 95% confidence intervals. The samples
will be collected from a population that displays a normal distribution with a population standard deviation of 108
and a population mean of 2130.