Problem 5 A random sample of 150 test scores has a sample me

(Problem 5) A random sample of 150 test scores has a sample mean of 80. Assume that the test scores have a population standard deviation of 15. Construct a 95% confidence interval estimate of the mean test scores. (10 points)

Solution

Note that              
              
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 =    80          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    15          
n = sample size =    150          
              
Thus,              
              
Lower bound =    77.59954416          
Upper bound =    82.40045584          
              
Thus, the confidence interval is              
              
(   77.59954416   ,   82.40045584   ) [ANSWER]