to estimate the mean of a moundshaped population a sample of

to estimate the mean of a mound-shaped population, a sample of 15 observations had mean 123.47 and a standard deviation 8.65. Calculate a 90% confidence interval estimate of the population mean. (show Work)

Solution

Note that              
Margin of Error E = t(alpha/2) * s / sqrt(n)              
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 =    0.05          
X = sample mean =    123.47          
t(alpha/2) = critical t for the confidence interval =    1.761310136          
s = sample standard deviation =    8.65          
n = sample size =    15          
df = n - 1 =    14          
Thus,              
Margin of Error E =    3.933745981          
Lower bound =    119.536254          
Upper bound =    127.403746          
              
Thus, the confidence interval is              
              
(   119.536254   ,   127.403746   ) [ANSWER]