Question

A POLYGRAPH (LIE DETECTOR) IS AN INSTRUMENT USED TO DETERMINE IF AN INDIVIDUAL IS TELLING THE TRUTH. THESE TESTS ARE CONSIDERED TO BE 95 % RELIABLE. IN OTHER WORDS, IF AN INDIVIDUAL LIES, THERE IS A .95 PROBABILITY THAT THE TEST WILL DETECT A LIE. LET THERE ALSO BE A .025 PROBABILITY THAT THE TEST ERRONEOUSLY DETECTS A LIE EVEN WHEN THE INDIVIDUAL IS ACTUALLY TELLING THE TRUTH. CONSIDER THE NULL HYPOTHESIS, "THE INDIVIDUAL IS TELLING THE TRUTH, THE ANSWER THE FOLLOWING QUESTIONS

WHAT IS THE POBABLITY OF A TYPE I ERROR?

WHAT IS THE PROBABILITY OF A TYPE II ERROR

Answer 1

Let us consider the hypothesis testing  

Type I error is the error when we reject the null hypothesis when it will be true

Type II error is the error, when we will accept  the null hypothesis when it will be false

Below considerations about the alternative hypotheses null hypothesis are given

There are two conditions

null hypothesis : the individual is telling the truth

alternate hypothesis: the individual is not telling the truth

which is shown in below table

Decision	Actual
	Lie	Truth
Detected	0.95	0.005 (Type 1 error) False lie (positive)
Not detected	1-0.9=0.05 (Type 11 error) False truth(Negative)	0.995
Type I error=0.005 P(Type I error)=0.005 Type II error =0.05 P(Type II)=1-P(Lie was called as lie)=1-0.95=0.05

As the type 1 error is incorrect reject null hypothesis so it is false lie call

As the type II error is incorrectly failing to reject null hypothesis so it false truth call

So the probability of Type I error is the probability of rejecting the null hypothesis, when it is true.

So, the probability of Type I error is probability that the lie detector detects a lie, while the person actually telling a truth.

Hence, the probability of Type I error is 0.005

Let us now discuss about type II error

The probability of Type II error is the probability of not rejecting the null hypothesis when it is false.

So the probability of Type II error is probability that the lie detector detects a truth while the person actually telling a lie.

Hence, the probability of Type II error is (100-95)%-=5%

Due to Type I error analyst wrongly  concludes that the person is telling a lie while the person actually telling a truth.

Due to Type II error analyst wrongly concludes that the person is telling a truth while the person actually telling a lie.

So We can not accept the null hypothesis but do not reject the null hypothesis

if there exists the consistency in sample evidence with the null hypothesis.

If we do not reject the null hypothesis So it means that it will not  prove that the individual is telling a truth.