A random sample of 81 items is taken producing a sample mean

A random sample of 81 items is taken producing a sample mean of 47 and a sample standard deviation of 5.89. Construct a 90% confidence interval to estimate the population mean.

Solution

Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=47
Standard deviation( sd )=5.89
Sample Size(n)=81
Confidence Interval = [ 47 ± t a/2 ( 5.89/ Sqrt ( 81) ) ]
= [ 47 - 1.664 * (0.654) , 47 + 1.664 * (0.654) ]
= [ 45.911,48.089 ]