Sample Data 500 650 600 505 450 550 515 495 650 395 Construc

Sample Data: 500, 650,. 600, 505, 450, 550, 515, 495, 650, 395 Construct a 95% confidence interval estimate of the population mean. ( you may assume that the original population is normally distributed.)

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 =    0.025          
X = sample mean =    531          
t(alpha/2) = critical t for the confidence interval =    2.262157163          
s = sample standard deviation =    82.7915723          
n = sample size =    10          
df = n - 1 =    9          
Thus,              
              
Lower bound =    471.774477          
Upper bound =    590.225523          
              
Thus, the confidence interval is              
              
(   471.774477   ,   590.225523   ) [ANSWER]