Answer:
66.600% to 68.600%
Explanation:
The formula for calculating confidence interval for a proportion is
p ± Z √(p(1-p)/n)
(p is p hat with ∧ over p)
p hat= number of events/ total number of attempts i.e. 25/37 = 0.676
Z=z i.e. alpha = 1-0.9 (from 90%) = 0.10
alpha/2= 0.10/2 = 0.05
z value for area of 0.0500 is o.13 (from z table)
putting these values in the above formula
0.676 ± 0.13 √(0.676(1-0.676)/37)
= 0.676 ±0.13(0.0769387)
=0.676± 0.10002034387
0.676+ 0.10002034387= 0.68600 or 68.600%
0.676-0.10002034387= 0.665998 or 66.600%
hence CI is 66.600% to 68.600%