The EPA states that corrective action must be taken if the amount of lead in a d
ID: 3323020 • Letter: T
Question
The EPA states that corrective action must be taken if the amount of lead in a drinking water supply exceeds 0.015 mg/L. suppose a water sample is taken and the following hypothesis test is performed.
H0 : u =.015
Ha= u less then 0.015
A) When preforming a statisical test of hypotheses, the researcher is in danger of making two different errors. these errors are labeled type 1 and type 2. define these error types.
B) for the hypothesis test stated above, explain what making a type 1 error would be?
C) for the hypothesis test stated above, expplain what a type 2 error would be.
D) for the hypothesis test above, which error type would have more severe consequences?
Explanation / Answer
The EPA states that corrective action must be taken if the amount of lead in a drinking water supply exceeds 0.015 mg/L. suppose a water sample is taken and the following hypothesis test is performed.
H0 : u =.015
Ha= u less then 0.015
A) There are two types of errors in statistical hypothesis testing,
1. Type 1 Error: The probability of type 1 error is denoted by .
The type 1 error is reject H0 when it is true.
It is more severe than type 2 error.
2. Type 2 Error: The probability of type 2 error is denoted by .
The type 2 error is, accept H0 when it is false.
B) In this problem we set Ho and Ha, Making type 1 error means H0 is true and still we are rejecting this H0.
It means the corrective action must be taken if the amount of lead in a drinking water supply exceeds 0.015mg/l but we are not taking any action, so it is risky.
C) In this problem we set Ho and Ha, Making type 2 error means H0 is false and still we are accepting this H0.
It means there is no need to take corrective action if the amount of lead in a drinking water supply exceed 0.015mgl but still we are taking action.
D) The above hypothesis, type 1 error is severe, because there is need to action but we are not taking so it risky.
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