Answer:
CI = ( 0, 042 ; 0,079 )
Step-by-step explanation:
If from 884 , 831 disks were OK then 884 - 831 = 53 were defective
x = 53
p = 53/884 p = 0,0599 or p = 5,99 % p ≈ 6 %
and q = 1 - 0,06 q = 0,94
p*n and q*n are big enough
For CI 98 % significance level is α = 2 % α/2 = 0,01
z(score) for α/2 = 0,01 is
z(c) ≈ 2,324
CI = p ± z(c) *√p*q/n
√p*q/n = √ ( 0,94*0,06)/884
√p*q/n = √ 0,0564/884
√p*q/n = 0,00799
CI = ( 0,06 ± 2,324*0,00799)
CI = ( 0,06 - 0,0185 ; 0,06 + 0,0185 )
CI = ( 0, 042 ; 0,079 )
