Question

State the null and alternative hypothesis in each case. (a) A hypothesis test will be used to potentially provide evidence that the population mean is more than 10. (b) A hypothesis test will be used to potentially provide evidence that the population mean is not equal to 7. (c) A hypothesis test will be used to potentially provide evidence that the population mean is less than 5

Answer 1

a) Null hypothesis:
`\mu \leq 10`

Alternative hypothesis:
`\mu >10`

b) Null hypothesis:
`\mu = 7`

Alternative hypothesis:
`\mu \\eq 7`

c) Null hypothesis:
`\mu \geq 5`

Alternative hypothesis:
`\mu <5`

Explanation:

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".

Based on this we can answer the question.

Part a

The system of hypothesis for this case would be:

Null hypothesis:
`\mu \leq 10`

Alternative hypothesis:
`\mu >10`

Would be a upper right tailed test on this case.

Part b

The system of hypothesis for this case would be:

Null hypothesis:
`\mu = 7`

Alternative hypothesis:
`\mu \\eq 7`

Would be a two tailed test on this case.

Part c

The system of hypothesis for this case would be:

Null hypothesis:
`\mu \geq 5`

Alternative hypothesis:
`\mu <5`

Would be a lower left tailed test on this case.