Question

State whether each set of hypothesis is valid for a statistical test and briefly explain why ?

Answer 1

Complete Question:

State whether each set of hypothesis is valid for a statistical test and briefly explain why ?

`H_0 : \mu=10; \ \ \ H_a : \mu\\e10`

`H_0 : p \\e 0.5; \ \ \ H_a : p = 0.5`

`H_0 : p_1 < p_2; \ \ \ H_a : p_1 \supset p_2`

Answer:

`H_0 : \mu=10; \ \ \ H_a : \mu\\e10` --- Valid

`H_0 : p \\e 0.5; \ \ \ H_a : p = 0.5` --- Invalid

`H_0 : p_1 < p_2; \ \ \ H_a : p_1 \supset p_2` --- Invalid

Explanation:

For a test of hypothesis to be valid, the null hypothesis has to contain some form of equality i.e.
`=, \le,\ or\ \ge`

So, the above will be used to test for validity in the given tests of hypotheses.

`H_0 : \mu=10; \ \ \ H_a : \mu\\e10`

This is valid because the null hypothesis has an equality sign.

The null hypothesis is:
`H_0:\mu = 10`

`H_0 : p \\e 0.5; \ \ \ H_a : p = 0.5`

This is invalid because the null hypothesis does not have any equality sign. The null hypothesis is:
`H_0:p \\e 0.5`

`H_0 : p_1 < p_2; \ \ \ H_a : p_1 \supset p_2`

This is invalid because the null hypothesis does not have any equality sign. The null hypothesis is:
`H_0:p_1 <p_2`