A sample of 64 observations is taken from a normal populatio

A sample of 64 observations is taken from a normal population with a standard deviation of 10.The sample mean is 80.Determine the 99% Confidence Interval for the population mean?

Given in the problem:

n = 64

  = 80

= 10

Confidence Interval = 99%

What is the Relevant formula for a population mean with a known :

Determine the 99% Confidence Interval for the population mean

Solution

Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
    x    = Mean
    sd   = Standard Deviation
    a    = 1 - (Confidence Level/100)
    Za/2 = Z-table value
    CI   = Confidence Interval
Mean(x)=80
Standard deviation( sd )=10
Sample Size(n)=64
Confidence Interval = [ 80 ± Z a/2 ( 10/ Sqrt ( 64) ) ]
= [ 80 - 2.58 * (1.25) , 80 + 2.58 * (1.25) ]
= [ 76.775,83.225 ]