Question

choose the best description and example of the alternative hypothesis in a hypothesis test. a statistical hypothesis that there is a difference between a parameter and a certain value, or between two parameters. example: $h_{1}: p_{1}78$. a statistical hypothesis that there is an alternative to a certain parameter, or to two parameters. example: $h_{1}: p_{1}$ is either 0.76 or 0.79. a statistical hypothesis that there is no difference between a parameter and a certain value, or between two parameters. example: $h_{1}: p_{1}=p_{2}$

Explanation:

The alternative hypothesis \(H_1\) is a statistical hypothesis that there is a difference between a parameter and a certain value, or between two parameters. It is the claim we are trying to find evidence for. In hypothesis testing, the null hypothesis \(H_0\) represents the status - quo or no - difference claim. The first option correctly defines the alternative hypothesis as a claim of difference (e.g., \(H_1:p_1 < p_2\) shows a difference between two population proportions \(p_1\) and \(p_2\)).
The second option is incorrect because the alternative hypothesis is not just the opposite of the null in a simple greater - than/less - than sense when the null is not in the form \(H_0:\theta=\theta_0\) (the null hypothesis should be a statement of equality in the standard hypothesis - testing framework). The third option is incorrect as the alternative hypothesis is not about a parameter taking on one of two specific non - equality values in the way described. The fourth option is incorrect because \(H_1:p_1 = p_2\) would be a null - like (equality) statement, and the alternative hypothesis is about non - equality.

Answer:

A statistical hypothesis that there is a difference between a parameter and a certain value, or between two parameters. Example: \(H_1:p_1 < p_2\)