Final answer:
The larger n is, the closer the t distribution resembles the z distribution, which is true due to the effects described by the central limit theorem. The statement is true.
Step-by-step explanation:
True. The statement is correct: the larger n is, the closer the t distribution looks to the z distribution. This is due to the central limit theorem, which indicates that as the sample size increases, the sampling distribution of the means becomes more normal.
This is why we observe that the t distribution starts to resemble the standard normal (z) distribution more closely with an increase in degrees of freedom (which is one less than the sample size).
The Student's t distribution has more probability in the tails and is therefore a bit wider than the standard normal distribution, particularly with fewer degrees of freedom.
However, as the degrees of freedom increase, the extra probability in the tails diminishes, and the t distribution becomes narrower, approaching the shape of the normal distribution. This eventually leads to an approximate equivalence between the areas under the respective curves, as sample size (n) gets large.