Final answer:
It is true that we cannot prove a null hypothesis in hypothesis testing. We only decide whether there is enough evidence to reject it based on the concept of falsifiability and probabilities, which avoids proving the null hypothesis true.
Step-by-step explanation:
The statement, 'In hypothesis testing we cannot prove a null hypothesis is true', is true. The essence of hypothesis testing is to decide whether there is enough evidence to reject the null hypothesis, not to prove it true. The null hypothesis is an assumption that there is no effect or no difference, and it is used as a starting point for scientific inquiry.
Hypothesis tests are based on probability laws and the concept of falsifiability. We test if the data collected is so unlikely under the null hypothesis that we have sufficient grounds to reject it. If we cannot reject the null hypothesis, it does not mean that the null hypothesis is proven true; it simply means there is not enough evidence against it. This is partly because of the potential for Type 1 and Type 2 errors in hypothesis testing.
Additionally, data that does not support a hypothesis can still be useful because it helps refine scientific understanding and improve experimental design. Hence, rare events observed in the data may lead us to question the null hypothesis and, potentially, support the alternative hypothesis.