Testing for Alzheimer’s disease can be a long and expensive process, consisting

Question

Testing for Alzheimer’s disease can be a long and expensive process,
consisting of lengthy tests and medical diagnoses. Some physicians use theFolstein test20, a brief, 30 second neurocognitive test to serve as a quick screen forpossibility of the disease for senior citizens. A score below 25 raises concerns andmay trigger an order for a more exhaustive battery of tests.

(a) Is this a one-tailed or a two-tailed test? Explain.

(b) Write the null and alternative hypotheses.

(c) In this context, what would a Type I error be?    What are the consequences?

(d) In this context, what would a Type II error be?    What are the consequences?(e) Which error type is more serious?   Explain.

Explanation / Answer

(a)

Test is one tailed (left tailed).

(b)

Hypotheses are:

H0: The person has Alzheimer’s disease.

Ha:  The person does not have Alzheimer’s disease (that is score is less than 25).

(c)

The type I error is the probability of rejecting the true null hypothesis. That is reseacher incoorectly conclude that patient do not have disease while actually patient has.

The consequences is "Patient will not get treatment while actually he/she needed it".

(d)

The type II error is the probability of fail to reject the false null hypothesis. That is reseacher incoorectly conclude that patient has disease while actually patient do not have.

The consequences is "Patient will go a more exhaustive battery of tests while actually he/she do not need it".

(e)

Type I error is more serious.

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