A study was conducted in which rats showed compassion by freeing a trapped rat. In the study, all six of the six female rats showed compassion by freeing the trapped rat while 17 of the 24 male rats did so. We found a 95% confidence interval for the difference in proportion of rats showing compassion, using the proportion of female rats minus the proportion of male rats, to be 0.104 to 0.480. In testing whether there is a difference in these two proportions:

What are the null and alternative hypotheses?

The null hypothesis that there is no significant evidence to conclude that there is a significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.

That is, there is no significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.

H₀: μ₀ = 0

or

H₀: p₁ = p₂

And the alternative hypothesis that there is evidence that the proportion of female rats that show compassion is significantly different from the proportion of male rats that show compassion.

That is, there is a significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.

Hₐ: μ₀ ≠ 0

or

Hₐ: p₁ ≠ p₂

Step-by-step explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and is usually about the absence of significant difference between two proportions being compared. It usually maintains that random chance is responsible for the outcome or results of any experimental study/hypothesis testing. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It proposes that there is indeed a significant difference between two proportions being compared. It usually confirms the theory being tested by the experimental setup.

It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, we want to check whether there is a significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.

If the proportion of female rats that show compassion = p₁

And

If the proportion of male rats that show compassion = p₂

And the difference between them is given as

μ₀ = p₁ - p₂

The null hypothesis and alternative hypothesis can be expressed as: