Finite Math Examples

$H^{0} = 5$

Step 1

Find $H_{a}$ (the alternative hypothesis) for the given null hypothesis $H_{0}$ .

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Step 1.1

The null hypothesis must always include the concept of equality, which means that it must include the operators equal, less or equal, or greater or equal. On the other hand, the alternative hypothesis must always express the opposite of the operator used for the null hypothesis, which means it should always include not equal, greater than, or less than.

Null hypothesis:

It must always include equal operator, less than operator, or greater or equal operator.

Alternative hypothesis:

If the null expresses equal operator, the alternative expresses not equal operator.

If the null expresses less or equal, the alternative expresses greater than.

If the null expresses greater or equal, the alternative expresses less than.

Step 1.2

The alternative hypothesis $H_{a}$ or $H_{1}$ must always express the opposite of the operator used for the null hypothesis $H_{0}$ . In this case, the opposite of $H_{0} = 5$ is $H_{a} \neq 5$ .

$H_{a} \neq 5$

Step 2

Depending on the alternative hypothesis operator, greater than operator will be a right tailed test, less than operator is a left tailed test, and not equal operator is a two tailed test.

Alternative hypothesis has the greater than operator, right tailed test.

Alternative hypothesis has the less than operator, left tailed test.

Alternative hypothesis has the not equal operator, two tailed (left and right) test.

Step 3

The alternative hypothesis operator is not equal which gives a two tailed test.

Two tailed test