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.作者: kim226 时间: 2013-4-3 22:05
should be b作者: Maddin 时间: 2013-4-3 22:11
can anyone explain why? perhaps a better explanation than the book gives.作者: hardwork24 时间: 2013-4-3 22:13
Ya B is pretty straight forward.作者: rkapoor 时间: 2013-4-3 22:15
“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. ”
I agree with you I don’t understand it either. Can anyone else explain this without just saying “ya it’s B”. We know it’s B, we want to know WHY. Thanks作者: Ionutzakis 时间: 2013-4-3 22:18
wch239,
the way i see it (and any feedback is appreciated) after looking back at the problem is that as degrees of freedom increases, the sample n increases, making the sample variance more “accurate.” this means that the sample variance approaches the population variance; not zero. that’s why the book says, “As the degrees of freedom get larger, the tdistribution approaches the normal distribution.” therefore this makes B), which says that the variance approaches zero, an incorrect statement.作者: jawz 时间: 2013-4-3 22:20
That makes sense. I didn’t research this at all, but I like to try to understand all questions being asked on here it’s the only way I can study at work.
