Question

true or false? a 25-year-old man complains of chest pain. he wants to be admitted by a hospital as a patient because he believes he has a heart attack. heart attacks in the 25-year-old men are rare, and medical treatments on heart attacks are expensive in the hospital. for a given test on whether the man has a heart attack, we state the null hypothesis to be that the man has no heart attack. the probability of making a type ii error is: p(the hospital does not admit him as a heart attack patient | the man has a heart attack).

Answer 1

The null hypothesis to be that the man has no heart attack. the probability of making a type ii error is: true

Define the type-ii error in the context of hypothesis testing as

Type -ii error

Not rejecting the null hypothesis ($m_{0}$); When $m_{0}$ is actually false

Therefore P(Type-ii error)

=P[Not rejecting $m_{0}$/$m_{0}$ is actually false]

In the given scenario; the null and alternative hypothesis are defined as

$m_{0}$: the man has no heart attack

$m_{1}$: the has a heart attack

Now, the probability of committing a type-ii error, can be defined as

P(Type-ii error) = P[The hospital does not admit him as a heart attack patient(i.e., $m_{0}$ is not rejected) | the man has a heart attack (i.e., $m_{0}$ is actually false)]

Hence, the given statement is true.

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