Question

Criminal investigators use biometric matching for fingerprint recognition, facial recognition, and iris recognition. When matching fingerprints, each subject is given a mean match score for how well their fingerprint matches the given fingerprint, based on different criteria. There are six criteria used to calculate the match score. The mean match score used by a particular police department is 80. If the police department finds a higher match score than this number, they consider the person a fingerprint match and a suspect in the crime. The null hypothesis is that the mean match score is 80. The alternative hypothesis is that the mean match score is greater than 80. Is the following a Type I error or a Type II error or neither? The test shows that the mean match score is more than 80 when the person does not actually have a fingerprint match.

Answer 1

It is not a Type I error neither a Type II error.

Explanation:

Let
`\mu` be the true mean match score. The null hypothesis is
`H_(0): \mu = 80` and the alternative hypothesis is
`H_(1): \mu > 80` (upper-tail alternative). When the test shows that the mean match score is more than 80 when actually is equal to 80 a Type I error is made. On the other hand, when the test shows that the mean match score is equal to 80 when actually is more than 80 a type II error is made. Therefore, when the test shows that the mean match score is more than 80 when the person does not actually have a fingerprint match, does not correspond to a Type I error neither to a Type II error.