Salaries of 40 college graduates who took a statistics cours

Salaries of 40 college graduates who took a statistics course in college have a mean, x , of $ 68,200. Assuming a standard deviation, , of $18,561, construct a 95% confidence interval for estimating the population mean .

$___ <   < $___

Round to the nearest integer as needed.

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)=68200
Standard deviation( sd )=18561
Sample Size(n)=40
Confidence Interval = [ 68200 ± Z a/2 ( 18561/ Sqrt ( 40) ) ]
= [ 68200 - 1.96 * (2934.752) , 68200 + 1.96 * (2934.752) ]
= [ 62447.887,73952.113 ]

= [ 62448 ,73953 ]