The first thing to do when given a claim is to write the claim mathematically (if possible), and decide whether the given claim is the null or alternative hypothesis. If the given claim contains equality, or a statement of no change from the given or accepted condition, then it is the null hypothesis, otherwise, if it represents change, it is the alternative hypothesis.

The following example is not a mathematical example, but may help introduce the concept.

Example

"He's dead, Jim," said Dr. McCoy to Captain Kirk.

Mr. Spock, as the science officer, is put in charge of statistically determining the correctness of Bones' statement and deciding the fate of the crew member (to vaporize or try to revive)

His first step is to arrive at the hypothesis to be tested.

Does the statement represent a change in previous condition?

Yes, there is change, thus it is the alternative hypothesis, H_{1}

No, there is no change, therefore is the null hypothesis, H_{0}

The correct answer is that there is change. Dead represents a change from the accepted state of alive. The null hypothesis always represents no change. Therefore, the hypotheses are:

H_{0} : Patient is alive.

H_{1} : Patient is not alive (dead).

States of nature are something that you, as a statistician have no control over. Either it is, or it isn't. This represents the true nature of things.

Possible states of nature(Based on H_{0})

Patient is alive (H_{0} true - H_{1} false )

Patient is dead (H_{0} false - H_{1} true)

Decisions are something that you have control over. You may make a correct decision or an incorrect decision. It depends on the state of nature as to whether your decision is correct or in error.

Apr 21st, 2015

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