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 ?

$H_0 : \mu=10; \ \ \ H_a : \mu\ne10$

$H_0 : p \ne 0.5; \ \ \ H_a : p = 0.5$

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

Answer:

$H_0 : \mu=10; \ \ \ H_a : \mu\ne10$ --- Valid

$H_0 : p \ne 0.5; \ \ \ H_a : p = 0.5$ --- Invalid

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

Step-by-step 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.

$H_0 : \mu=10; \ \ \ H_a : \mu\ne10$

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

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

$H_0 : p \ne 0.5; \ \ \ H_a : p = 0.5$

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

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

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