The number of unhealthy days based on the AQI Ai Quality Ind

The number of unhealthy days based on the AQI (Ai, Quality Index) for a random sample of metroplotan areas is shown. Construct a 99% confidence interval for the true mean based on the data.

Solution

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.005          
X = sample mean =    33.5          
t(alpha/2) = critical t for the confidence interval =    3.249835542          
s = sample standard deviation =    27.67770864          
n = sample size =    10          
df = n - 1 =    9          
Thus,              
              
Lower bound =    5.055944508          
Upper bound =    61.94405549          
              
Thus, the confidence interval is              
              
(   5.055944508   ,   61.94405549   ) [ANSWER]