The null hypothesis ($H_0$) for a test of the difference of means for two independent populations can be expressed in two equivalent ways:

1. $H_0: \mu_1 = \mu_2$ (the means of the two populations are equal).
2. $H_0: \mu_1 - \mu_2 = 0$ (the difference between the means of the two populations is zero).

From the provided options, the correct answer is:

$H_0: \mu_1 = \mu_2$ or $H_0: \mu_1 - \mu_2 = 0$

This corresponds to the second option in the image.

Would you like me to explain why the null hypothesis is stated this way or how to test it?

Here are five related questions to consider:

1. What are the alternative hypotheses ($H_a$) in such tests?
2. How do we calculate the test statistic for the difference in means?
3. What assumptions must be met for a valid hypothesis test of two means?
4. How do sample sizes affect the outcome of this hypothesis test?
5. What is the role of confidence intervals in interpreting hypothesis test results?

Tip: Always verify the assumptions (e.g., normality, equal variances) when performing a hypothesis test on population means.