Final answer:
The statement is false; the t distribution has thicker tails and is less concentrated around the mean compared to the z distribution. It approaches the z distribution as the degrees of freedom increase.
Step-by-step explanation:
The statement that the t distribution is taller and thinner (more concentrated around the mean) than the z distribution is false. The t distribution actually has more probability in its tails and is less concentrated around the mean, especially when the number of degrees of freedom is small. This means that the t distribution has thicker tails and is shorter in the center compared to the standard normal (z) distribution. As the degrees of freedom increase, the t distribution approaches the z distribution in shape. With enough degrees of freedom (usually > 30), they are nearly indistinguishable.
Comparing the t distribution with 15 degrees of freedom to the standard normal distribution, the t distribution will appear to have thicker tails and a lower peak. However, it is important to note that the t distribution approaches the standard normal distribution as the sample size (degrees of freedom) gets larger.
The F distribution is related but distinct, used primarily in ANOVA testing, and exhibits a different shape, being right-skewed with characteristics dependent on the degrees of freedom of the numerator and denominator.