Question

In §9.2 the concepts of Type I and Type II errors are introduced. Consider the situation where a husband and wife go to the doctor’s office to each get some tests run and the doctor accidentally mixes up their charts. The doctor comes into the exam room with the results of the tests and declares that the wife is NOT pregnant but her husband IS indeed pregnant with a baby.

How does this illustrate the concepts behind Type I and Type II errors? Make sure to state your null hypothesis for this situation when discussing error

Answer 1

Type I error :- when a null hypothesis is rejected and the alternative hypothesis is accepted ,even if the null hypothesis is true, then there is a case of type I error.

Type II error :- when a null hypothesis is accepted and the alternative hypothesis is rejected , even if null hypothesis is false, then it is a case of type II error.

As per the case described here, the reports of husband and wife got mixed up stating that husband is pregnant with baby and wife is not pregnant .

We know that it is not possible biologically that husband or the man is pregnant .

So, we will take

null hypothesis as man is not pregnant

Alternative hypothesis as man is pregnant

As per the doctors report in this case , the null hypothesis is rejected

So, this is a case of type I error when a true null hypothesis is rejected.

Now we Will take

Null hypothesis as man is pregnant

Alternative hypothesis as man is not pregnant

So, here as per the doctor's report man is pregnant . So, null hypothesis is true as per doctors report.

This is a case of type II error as a false null hypothesis is accepted by the doctor.