Fortynine items are randomly selected from a population of 5

Forty-nine items are randomly selected from a population of 500 items. The sample mean is 40 and the sample standard deviation 9.

Develop a 99% confidence interval for the population mean. (Round your answers to 3 decimal places.)

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 =    0.005          
X = sample mean =    40          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    9          
n = sample size =    500          
              
Thus,              
Margin of Error E =    1.036751296          
Lower bound =    38.9632487          
Upper bound =    41.0367513          
              
Thus, the confidence interval is              
              
(   38.9632487   ,   41.0367513   ) [ANSWER]