One original lest of extrasensory perception ESP involves us

One original lest of extrasensory perception (ESP) involves using Zener cards. Each card shows one of five different symbols (square, circle, star, wavy lines, cross). One person randomly picks a card and concentrates on the symbol it shows. A second person, in another room, tries to identify the symbol that was selected. Chance performance on this task (just guessing) should lead to correct identification of about one in five cards. A psychologist used the Zener cards to evaluate a sample of n = 9 subjects who claimed to have ESP. Each subject was tested on a series of 100 cards, and the number correct for the 9 subjects is as follows: 18, 24, 22, 19, 28, 15, 26, 25, 23 (sample mean x = 22.22, sample standard deviation s = 4.18). Use a 95% confidence interval to estimate the value of the population mean.

Solution

19.

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 =    0.025          
X = sample mean =    22.22222222          
t(alpha/2) = critical t for the confidence interval =    2.306004135          
s = sample standard deviation =    4.176654695          
n = sample size =    9          
df = n - 1 =    8          
Thus,              
              
Lower bound =    19.01176122          
Upper bound =    25.43268322          
              
Thus, the confidence interval is              
              
(   19.01   ,   25.43   ) [ANSWER, C]