Answer:
a) Type 1 Error: 1.5%
b) Type 2 Error: 5.5%
Step-by-step explanation:
Probability of positive reaction when infact the person has disease = 94.5%
This means, the probability of negative reaction when infact the person has disease = 100- 94.5% = 5.5%
Probability of positive reaction when the person does not have the disease = 1.5%
This means,
Probability of negative reaction when the person does not have disease = 100% - 1.5% = 98.5%
Our Null Hypothesis is:
"The individuals does not have the disease"
Part a) Probability of Type 1 Error:
Type 1 error is defined as: Rejecting the null hypothesis when infact it is true. Therefore, in this case the Type 1 error will be:
Saying that the individual have the disease(positive reaction) when infact the individual does not have the disease. This means giving a positive reaction when the person does not have the disease.
From the above data, we can see that the probability of this event is 1.5%. Therefore, the probability of Type 1 error is 1.5%
Part b) Probability of Type 2 Error:
Type 2 error is defined as: Accepting the null hypothesis when infact it is false. Therefore, in this case the Type 2 error will be:
Saying that the individual does not have the disease(negative reaction) when infact the individual have the disease.
From the above data we can see that the probability of this event is 5.5%. Therefore, the probability of Type 2 error is 5.5%
