Question

Basic Computation: Setting Hypotheses Suppose you want to test the claim that a population mean equals 30 .

(a) State the null hypothesis. ___________________________
(b) State the alternate hypothesis if you have no information regarding how the population mean might differ from 30. _________________
(c) State the alternate hypothesis if you believe (based on experience or past studies) that the population mean may be greater than 30. _______________
(d) State the alternate hypothesis if you believe (based on experience or past studies) that the population mean may not be as large as 30. ______________

Answer 1

Part a

Null hypothesis:
`\mu =30`

Part b

Alternative hypothesis:
`\mu \\eq 30`

Part c

Alternative hypothesis:
`\mu > 30`

Part d

Alternative hypothesis:
`\mu < 30`

Explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Solution to the problem

For this case we want to test if the true mean is equal to 30 or no.

Part a

Null hypothesis:
`\mu =30`

Part b

Alternative hypothesis:
`\mu \\eq 30`

Part c

Alternative hypothesis:
`\mu > 30`

Part d

Alternative hypothesis:
`\mu < 30`