10 A random sample of 90 observations produced a sample mean

10. A random sample of 90 observations produced a sample mean (X-bar) of 25.9 and

a standard deviation s = 2.7. Find an approximate 95% confidence interval for the population mean µ. ____________________________________________

Solution

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    25.9          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    2.7          
n = sample size =    90          
              
Thus,              
Margin of Error E =    0.557815529          
Lower bound =    25.34218447          
Upper bound =    26.45781553          
              
Thus, the confidence interval is              
              
(   25.34218447   ,   26.45781553   ) [ANSWER]