In addition to teachers and administrative staff schools als

In addition to teachers and administrative staff, schools also have many other employees, including bus drivers, custodians, and cafeteria workers. In Auburn, WA, the average hourly wage is $16.92 for bus drivers, $17.65 for custodians, and $12.86 for cafeteria workers. Suppose that a second school district employs n = 36 bus drivers who earn an average of $14.75 per hour with a standard deviation of s = $2.85. Find a 95% confidence interval for the average hourly wage of bus drivers in school districts similar to this one.

$ ________ to $ _________

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)=14.75
Standard deviation( sd )=2.85
Sample Size(n)=36
Confidence Interval = [ 14.75 ± t a/2 ( 2.85/ Sqrt ( 36) ) ]
= [ 14.75 - 2.03 * (0.475) , 14.75 + 2.03 * (0.475) ]
= [ 13.786,15.714 ]