Pg. 294 (Reading 10)
#15. Which of the following is least likely a property of Student’s tdistribution?
A. It is symmetrical
B. As the degrees of freedom get larger, the variance approaches zero.
C. It is defined by a single parameter, the degrees of freedom, which is equal to n1
D. It has more probability in the tails and less at the peak than a standard normal distribution.
Personally, I feel that all of these statements are correct. Answer Key says that the answer is B, only saying “As the degrees of freedom get larger, the tdistribution approaches the normal distribution.”
I don’t really understand this. The formula for variance of the sample means = (sd squared)/n. Therefore, doesn’t it make sense that as degrees of freedom get larger, that also means n gets larger, making the right side of the equation (and thus the left side i.e. the variance) also approach zero? This would make choice B a true statement.
This calculation also intuitively makes sense, since the greater the sample size is (the more n’s), the smaller the variance should get since the sample mean approaches the population mean.
Thanks in advance to anyone who can help out. |
发表于 2013-4-3 22:03
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