The number of unhealthy days based on the AQI Air Quality In

The number of unhealthy days based on the AQI (Air Quality Index) for a random sample of metropolitan areas is shown. Construct a 98% confidence interval based on the data.

61           12          6          40          27          38          93          5          13          40          34                29           48         83   

Solution

sample size= 14

sample mean=37.78571

sample standard deviation =26.77306

The degree of freedom =n-1=14-1=13

Given a=1-0.98=0.02, t(0.01, df=13) =2.65 (from student t table)

So the lower bound is

xbar - t*s/vn=37.78571 - 2.65*26.77306/sqrt(14) =18.8239

So the upper bound is

xbar + t*s/vn=37.78571 + 2.65*26.77306/sqrt(14) =56.74752