Final answer:
As the sample size increases, the correlation needed for statistical significance decreases due to increased statistical power and reduced variability. Therefore, the correct answer is: b. it also gets smaller
Step-by-step explanation:
The question is about how the sample size affects the correlation needed for significance in statistical hypothesis testing. As the sample size increases, the size of the correlation necessary for statistical significance generally decreases.
This occurs because larger sample sizes tend to have more statistical power and a smaller standard error, which makes it easier to detect an effect or correlation if there is one.
For instance, with a smaller sample size, there is more variability, and therefore a larger correlation might be needed to be confident that the observed effect is not due to chance. As the sample size grows, the standard deviation of the sampling distribution of the means will decrease, and the confidence level would increase, though we would require a larger interval (summary c and f).
Moreover, with larger samples, there's a smaller sampling variability, and the results are more likely to be closer to the population average, leading to a more reliable statistic (Think about what contributes to making Doreen's and Jung's samples different).
Therefore, the correct answer is: b. it also gets smaller