16 Flashcards
Central limit theorem?
If you have independent random variables, then the sampling distribution, X bar_n, will approach a normal distribution with mean mu and variables (sigma)^2/n, AS sample size (n) increases
When you take the variance of the sampling distribution of the means of k values, then the variance of one value is the same as?
Variance of the mean of k values/k
The mean of the distribution of the means of k values is equal to?
The mean of 1 value.
If the original population is normal, then the central limit theorem works regardless of?
The sample size.
If the original distribution looks like a mountain from a histogram, no outliers or long tails, then?
You can get away when n >= 30 and treat the sample mean approximately normal
Conditions to guarantee that the central limit theorem always work?
•Finite mean,
•finite standard deviation,
•values are bounded (but some non bounded distributions can also work)
Sample proportions are approximately?
Normal
Sample variance?
The estimator of variance where the sum of standard deviations of X_i from the mean of X divided by one less than the sample size.
In a sample variance, if the original population is drawn as normal, then the estimator of sample variance is?
Something related to a chi^2 distribution
If you take a bunch of means of the estimator of sample variance (s^2), then you get?
Close to the actual variance since s^2 is unbiased for sigma^2
Which is biased, s^ ^2 or s^2?
s^ ^2 as it underestimates on average. This occurs when the sum of the squared deviations are divided by just n.
!!!Sample standard deviation?
Sample quantiles
Random sample size of n from population with quantiles Q_p, 0 < p < 1, then there are point estimators for Q_p as Q^_p.
In sample mean, the sample size n determines?
How many values to average where n = k.
