Answer:
(a) Find the probability of type I error. = 0.1018
Step-by-step explanation:
check attachment for the answer
Answer:
The probability of Type I error is = 0.10185.
Step-by-step explanation:
Solution:-
The type I - error is defined as the probability of rejecting Null hypothesis defined by Alternate hypothesis:
             Ha : X ≥ 8
Where,
X : Denote the number of cars crash with no visible damage
The random variate "X" is defined by binomial distribution:
              X ~ B ( n = 20 , p = 0.25 )
- The probability of Type I error:
            P (Type I error ) = P ( Reject Null hypothesis )
                          = P ( X ≥ 8 )
- The probability mass function of binomial random variate "X" is given:
           [tex]P ( X = x ) = nCr (p)^r * (1-p)^(^n^-^r^)\\P ( X \geq 8 ) = 1 - P ( X < 8 )\\\\P ( X \geq 8 ) = 1 - [ P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 ) + P ( X = 4 ) + P ( X = 5 ) + P ( X = 6 ) + P ( X = 7 ) ][/tex][tex]P ( X \geq 8 ) = 1 - [ (0.75)^2^0 + 20(0.25)*(0.75)^1^9 + 20C2(0.25)^2*(0.75)^1^8 +\\\\ 20C3(0.25)^3*(0.75)^1^7 + 20C4(0.25)^4*(0.75)^1^6 + 20C5(0.25)^5*(0.75)^1^5\\\\ + 20C6(0.25)^6*(0.75)^1^4 + 20C7(0.25)^7*(0.75)^1^3 ] \\\\\\P ( X \geq 8 ) = 1 - [ 0.00317 + 0.02114 + 0.06694 + 0.13389 + 0.18968 + 0.20233\\\\+ 0.16860 + 0.11240]\\\\P ( X \geq 8 ) = 1 - 0.89815 = 0.10185[/tex]
Answer: The probability of Type I error is = 0.10185.
