With large sample sizes, even small differences between the null value and the observed point estimate, a difference often called the effect size, will be identified as statistically significant.

Question

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The statement at hand concerns how statistical significance behaves as sample size grows. 
Option 1: True. When sample sizes become very large, even tiny differences between the null value and the observed estimate can yield small p-values because the standard error becomes very small. This means that test statistics (like z, t, or chi-square) can exceed the usual critical values even for minimal deviations, leading to statistical significance despite a small practical difference. In other words, the likelihood of rejecting the null increases with n, which makes tiny effects detectable as significant.
Option 2: False. This would be incorrect in light of the general principle just described. While it is true that large samples increase power and can make small effects statistically significant, it does not imply that significance is impossible for large samples or that all small differences are insignificant. The statement as written asserts that small differences will be identified as significant with large n, which aligns with standard statistical theory. The only caveat is that statistical significance does not imply large or important effect sizes; a result can be statistically significant but practically negligible if the sample size is huge. The wording does not dispute this nuance; it simply asserts the tendency, which is correct.
In summary, the statement reflects the well-known relationship between sample size and significance: larger samples can detect smaller differences as statistically significant, even if those differences are small in magnitude or potentially of limited practical importance.

FA25_QTM_100_3 5.30: True or false.

With large sample sizes, even small differences between the null value and the observed point estimate, a difference often called the effect size, will be identified as statistically significant.

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