How does the shape of a t-distribution change as the sample size increases? Explain.
a. As sample size increases, the sample variance more closely estimates the population variance. The result is that there is less variability in the tails of a t-distribution as the sample size increases—the tails approach the x-axis faster.
b. As sample size increases, the sample variance becomes less like the population variance. The result is that there is more variability in the tails of a t-distribution as the sample size increases—the tails approach the x-axis more slowly.
c. As sample size increases, the sample variance estimate of the population variance does not change. The result is that there is a constant amount of variability in the tails of a t-distribution as the sample size increases—the tails approach the x-axis at the same rate.
Answer: A
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