Final answer:
The correct answer is option b: If there is a treatment effect, it will have an average effect on the scores in the sample and produce a sample mean that is unlikely by random chance. This is based on the concept of rare events, where an observed sample mean far from the population mean suggests the treatment effect is significant and not due to chance.
Step-by-step explanation:
The subject of this question is a hypothesis test evaluating the effect of a treatment. The treatment effect on scores in a sample can manifest in different ways, but when it comes to hypothesis testing, the correct interpretation is that if there is a treatment effect, it will have an average effect on the scores in the sample and produce a sample mean that is unlikely to be drawn from the population by random chance (option b).
The reason for this is based on the concept of rare events in hypothesis testing. If the sample mean is considerably different from the population mean, it suggests that the observed effect is not due to random variation but is actually due to the treatment effect. The null hypothesis, which posits no treatment effect, is challenged if the observed sample mean is a rare event under the assumption that the null hypothesis is true.
Hypothesis testing can be conducted using either a z-test or a t-test, depending on whether the population standard deviation is known and if the sample comes from a normally distributed population or if the sample size is large. For a t-test, the sample standard deviation is used if the population standard deviation is unknown, and the sample should be a simple random sample that is approximately normally distributed.