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### What references should be cited to support using 30 as a large enough sample size?

I have read/heard many times that the sample size of at least 30 units is considered as "large sample" (normality assumptions of means usually approximately holds due to the CLT, ...). Therefore, in ...
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### Approximation error of confidence interval for the mean when $n \geq 30$

Let $\{X_i\}_{i=1}^n$ be a family of i.i.d. random variables taking values in $[0,1]$, having a mean $\mu$ and variance $\sigma^2$. A simple confidence interval for the mean, using $\sigma$ whenever ...
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### How useful is the CLT in applications?

My lecturer just covered the Lindeberg-Lévy central limit theorem and the multivariate version, the Lindeberg-Feller CLT. I understood the basic concept and I can derive it, etc. But it would help my ...
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### Repeated measures ANOVA or Friedman test?

I have a study with 35 subjects who received hypercoagulability testing at 4 different times (before surgery, after, at 1 week, and at 1 month). Each subject has 9 different test of hyper ...
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### Distribution of a sample from a normal population

If I were to collect ONE sample of size 20 from a normal population, how justified would I be in claiming that the sample is normally distributed? I'm getting a little confused since by the Central ...
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### If the parent distribution is skewed, but the sample size is greater than 30, is the distribution of the sample mean nearly Normal?

I have my AP Stats exam tomorrow and had this question. I apologize if it is too simplistic for this forum. I'm pretty sure the sample's distribution is nearly normal, but not 100%, can someone ...
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### Expected number of times the empirical mean will exceed a value

Given a sequence of i.i.d. random variables, say, $X_i \in [0,1]$ for $i = 1,2,...,n$, I'm trying to bound the expected number of times the empirical mean $\frac{1}{n}\sum_{i=1}^n X_i$ will exceed a ...
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### central limit theorem

can I do my statistics work based on the central limit theorem? I need to perform a t-test, ANOVA and multiple regression. my outcome variable is highly not normally distributed (Highly positively ...
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### Calculating means and confidence intervals when most data points are 0

I am looking at data set that has four groups. In each group, the data is mostly, 99+% of time, composed of zeros, but, when it is not zero it can be any float number (e.g., 0.01 to 921.2, with most ...
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### How often will sampling distribution of the mean not be normally distributed?

Kabacoff 2015 suggests that if we're not willing to assume the sampling distribution of the mean is normally distributed, we should use bootstrapping to estimate the sampling distribution of the mean. ...