What are two main reasons that can produce a high p-value?

A high p-value typically suggests that the evidence against the null hypothesis is weak. This can occur primarily due to two reasons:

Firstly, when the null hypothesis is true, any observed data or variation is essentially the result of random chance. In such a scenario, if the data collected aligns with the null hypothesis, it reflects the natural variability of the sample, contributing to a high p-value. This indicates that there is no statistically significant evidence to reject the null hypothesis since the results could easily happen by random sampling.

Secondly, a high p-value can arise when the effect size is small relative to the variability in the data. This situation may not yield sufficient evidence to suggest that any observed differences or effects are meaningful or significant. Thus, option B accurately portrays a situation where, if the null hypothesis is indeed true, the data might fortuitously appear to support it, leading to a high p-value.

The other options present scenarios that do not adequately reflect conditions leading to a high p-value. For instance, a large effect size in the context of a true null hypothesis would typically yield a low p-value because it would suggest a meaningful difference rather than supporting the null. Flawed data collection methods and small sample sizes can complicate interpretations but are not