The Professor's Response
Good Afternoon Mr. McGuckian,
I am reading Chapter 7.4 and in the part that says recall, I don't understand very well what the signs stands for or what it is trying to say.
I am referring to this part:
Recall: The CLT says if X ~ N(u,o^2 ), then X ~ N(u,o^2/n) for any sample size n—no matter how small.
I know we are talking about when to use the t-distribution and when not to use it (you use t when n is less than 30).. but I like to understand everything that is written on the notes... and I know the answer is probably super easy and that's why its embarrassing to ask.. but I would rather make sure I understand everything well.
Thank You Very Much
Adriana Nava
See the professor's answer below.
Hi Adriana,
That portion of the notes is just saying to recall that, the central limit theorem says, "If a random variable X has a normal distribution (with mean µ and variance sigma squared), then the sample means will be normally distributed (with mean µ and variance sigma squared divided by n). Basically, we are saying the sample means are normally distributed when the original data is normally distributed (this does not depend on the sample size). If the original data is not normal, we need to know the sample size is larger than 30 to assume the normality of the sample means. This is something that was stated in the central limit theorem from chapter 6.
I hope that helps,
Professor McGuckian