A columnist described the reliability of DNA paternity testing as follows: \"To

Question

A columnist described the reliability of DNA paternity testing as follows: "To get a completely accurate result, you would have to be tested, and so would (the man) and your mother. The test is 100 percent accurate if the man is not the father and 99.7 percent accurate if he is."

(a) Based on the information given, what are the values of , the probability of Type I error, and , the probability of Type II error?
= 1 ___
= 2 ___

(b) The columnist also stated, "If the mother is not tested, there is a 0.5 percent chance of a false positive." For the following hypotheses, what is the value of if the decision is based on DNA testing in which the mother is not tested?

H0: a particular man is the father
Ha: a particular man is not the father

= ___

You may need to use the appropriate table in Appendix A to answer this question.

Explanation / Answer

Null hypothesis: the man is the father

Alternate hypothesis: the man is NOT the father

Part a.

If the man is NOT the father and Null hypothesis is rejected, it is a correct decision 'Power' (1-beta = 1) => Beta = 0

If the man is the father and Null hypothesis is NOT rejected, it is a correct decision (1-alpha = 0.997) => Alpha = 0.003

Part b.

A False Positive is when Null hypothesis is true but it is Rejected => alpha = 0.005

Z-value for 1-alpha/2 is to be first calculated. Z(1-alpha/2) = Z(0.9975) = 2.81

Now, effect size (ES) from past data should be known. If unknown, consider 0.3 (It is the normal value and a conservative approximation)

Take M = ES*sqrt(ES/2) = 0.3*(sqrt(0.15)) = 0.1162

Z value corresponding to Power (1-Beta) = M - Z-value = 0.1162 - 2.81 = -2.6938

=> Power = 1 - Beta = 0.0036

=> Beta = 0.9964 [Answer]

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.