Question

Our hypothesis test is testing to see if there is a difference in the population mean between two groups. The data for each group has considerable variability. Given that there is considerable variability in the data for the two groups __________.

a. it will be easy to reject the null hypothesis of "no difference" with a small sample
b. it will be likely we don’t reject the null hypothesis of "no difference" with a small sample

Answer 1

Given that there is considerable variability in the data for the two groups b. it will be likely we don’t reject the null hypothesis of "no difference" with a small sample

What happens when variability is considerable ?

When there is considerable variability in the data for the two groups, it means that there is a wide spread of data points, and the data is more dispersed.

In hypothesis testing, a larger sample size is generally needed to detect a statistically significant difference when there is high variability in the data.

With a small sample size, it becomes more challenging to detect a true difference, and the likelihood of not rejecting the null hypothesis of "no difference" increases. A larger sample size provides more information and reduces the impact of variability.