Scores on the SAT Mathematics test SATM are believed to be n

Scores on the SAT Mathematics test (SAT-M) are believed to be normally distributed with mean . The scores of a random sample of seven students who recently took the exam are 550, 620, 480, 570, 690, 750, and 500. A 90% confidence interval for based on these data is:

A. (521.73, 666.85).

B. (532.86, 655.71).

C. (566.86, 621.71).

D. (502.91, 685.67).

Solution

a)

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 =    0.05          
X = sample mean =    594.2857143          
t(alpha/2) = critical t for the confidence interval =    1.943180281          
s = sample standard deviation =    98.80235201          
n = sample size =    7          
df = n - 1 =    6          
Thus,              
              
Lower bound =    521.73          
Upper bound =    666.85          
              
Thus, the confidence interval is              
              
(   521.73   ,   666.85   ) [ANSWER, A]