STATISTICS FINALS

• Central limit theorem

  -   If random samples of size n are drawn from a large or infinite population with mean µ and variance σ2, then the sampling distribution of the sample mean x is approximately normally distributed with mean µx = µ and standard deviation hence is a value of a standard normal variable Z
• Central limit theorem describes the shape of sampling distribution of mean.
• T distribution (student’s t distribution)

  -   Is a family of distributions that look almost identical to  the normal distribution curve, only a bit shorter and stouter.
• t=t score

  x=sample mean

  µ=population mean

  s= sample standard deviation

  n=sample size
• Degrees of freedom – the number of observations in a data set that are free to change without changing the mean. Maximum number of logically independent values which vary in the data sample.
• 1.  The distribution has mean o
• 1.  The distribution is symmetric about the mean.
• 1.    The variance is equal to df/df-2
• 1.  The variance is always greater than 1, but approaches 1 when df gets bigger.
• What if n approaches infinity? – the t distribution also approaches the standard normal distribution.
• Critical value is the number on the borderline separating sample statistics that are likely to occur from those that are unlikely to occur.
• Confidence interval is a range of values used to estimate the true value of the population parameter.
• 1.  The critical region appears at the top
• 1.  The degrees of freedom are on the leftmost section
• 1.  Confidence interval are at the bottom
• Percentile – a measure of position with data divided into 100 parts.