For this hypothesis test, the null and alternative hypotheses are given as:

• $H_0: \mu_1 = \mu_2$ (the means are equal)
• $H_a: \mu_1 > \mu_2$ (the mean of the first group is greater than the mean of the second group).

To represent the sample statistic for each simulated sample in a randomization distribution, we typically use the difference between the sample means. In this case, the notation to use would be:

$\bar{x}_1 - \bar{x}_2$

This notation represents the difference between the sample mean of the first group ($\bar{x}_1$) and the sample mean of the second group ($\bar{x}_2$).

Would you like further details or have any questions about this?

Here are some related questions to consider:

1. What is the purpose of using a randomization distribution in hypothesis testing?
2. How do you interpret a p-value in the context of a randomization test?
3. What are the assumptions underlying the hypothesis test used here?
4. How would you modify the test if the hypothesis was $H_a: \mu_1 < \mu_2$ instead?
5. What other types of sample statistics might be useful in hypothesis testing?

Tip: In hypothesis testing, always ensure that the assumptions of the test you are using are met to obtain valid results.