Respuesta :
(a) P( Type -I error) = P (rejecting [tex]H_0[/tex] | when [tex]H_0[/tex] is true )
(b) P( Type -II error)= P(not rejecting [tex]H_0[/tex] | when [tex]H_0[/tex] is false )
Given,
In the question:
We are interested in testing whether or not a coin is balanced based on the number of heads Y on 36 tosses of the coin.
To find the:
a) the value of α
b) the value of β if p = .7
Now, According to the question:
Hypothesis Testing:
The hypothesis testing evaluates two mutually exclusive statements about the population parameters to determine which statement is correct among them. There are two types of error :
1. Type -I
2. Type -II
The data is given as:
X ~ Bin(36, p)
[tex]H_0:p = 0.5\\\\H_1:p \neq 0.5[/tex]
(a) P( Type -I error) = P (rejecting [tex]H_0[/tex] | when [tex]H_0[/tex] is true )
= P(|X- 18| [tex]\geq[/tex] 4 ; p = 0.5)
= 1 - {P(14 < X < 22)}
= 1 - {P(X < 22) - P(X < 14)}
= 1 - {P(X ≤ 21) - P(X ≤ 13)}
= 1 - {0.87851 - 0.066249}
= 0.18774
(b) P( Type -II error)= P(not rejecting [tex]H_0[/tex] | when [tex]H_0[/tex] is false )
= P(|X- 18| [tex]>[/tex] 4 ; p = 0.7)
= P(14< X < 22)
= P(X < 22) - P(X < 14)
= P(X ≤ 21) - P(X ≤ 13)
= 0.091662 - 0.018322
= 0.07334
Learn more about Hypothesis Testing at:
https://brainly.com/question/16547400
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