Final answer:
The analyst may reject the null hypothesis if there is a significant difference in mean salary between samples of non-smokers and smokers, indicating that there might be a difference in earnings. Rejecting the null hypothesis suggests sufficient evidence to consider the alternative hypothesis as more likely, but does not absolutely prove it.
Step-by-step explanation:
When presented with a large difference in mean salary for samples of non-smokers and smokers, the analyst may be led to reject the null hypothesis. The null hypothesis here is that non-smokers earn the same as smokers. When the sample data does not support the null hypothesis (indicated by a significant salary difference), the analyst must decide whether the evidence is enough to favor the alternative hypothesis, which would claim that there is indeed a difference in earnings between non-smokers and smokers.
Hypothesis testing involves making decisions about the plausibility of hypotheses. If the sample evidence is strong enough against the null hypothesis, the analyst will reject it. It is important to note that rejecting the null hypothesis does not prove the alternative hypothesis absolutely; it simply suggests that there is sufficient evidence to consider it more likely.
Care must be taken to not make a Type I error, which is rejecting the null hypothesis (H0) when it is actually true. Likewise, we should avoid a Type II error, which is failing to reject H0 when it is false. The decision must be based on statistical evidence and significance levels determined before the hypothesis test.