The confidence interval is the probability that a value will fall between an upper and lower bound of a probability distribution, the value of a parameter lies within it. The margin of error is the range of values below and above the sample statistic in a confidence interval. Critical values is the point or points on the scale of the test statistic beyond which we reject the null hypothesis.
The central limit theorem says that the sampling distribution of any statistic will be normal or close to normal, if the sample size is large enough. The idea that a distribution of sample means is a more normal distribution than a distribution of scores, even when the population distribution is not normal. The central limit theorem should be used to identify characteristics of a sampling distribution. This theorem relates every distribution to the normal distribution.
Normal distributions are a family of distributions with a symmetrical bell shape. A normal distribution is determined by two parameters the mean and the variance. Normal distributions do not necessarily have the same means and standard deviations. A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. Normal distributions can have any mean and any (positive) standard deviation. The standard normal distribution is just a normal distribution scaled/standardized by the z-formula. The probability of any value xi under the normal distribution and the standard distribution is the same.
A discrete random variable can only take distinct, separate random variables, where as a continuous random variable can take any value within an interval and it has an infinite number of possible values. The probability distribution of a discrete random variable assigns probabilities to points while that of a continuous random variable assigns probabilities to intervals.
A binomial experiments is a statistical excitement that consists of repeated trials, and each trial can rusty in only two outcomes. One is called a success and the ot...