Stats reviewer

• Estimate

  is the value of range of value, that approximates the population value
• Point Estimate

  Is a specific numerical value of a population parameter. The sample mean X is the best estimate of a population mean
• Interval estimate

  Also called as confidence interval, is a range of values used to estimate a parameter.
• Confidence level

  Is the probability that the interval estimate will contain the trues population parameter.
• Critical value

  Also known as confidence coefficient, are the z-values that is used in describing the characteristics of a target population. When (PSD) is known, z-values are used.
• 90% confidence

  z = ±1.65
• 95% confidence

  z = ±1.96
• 99% confidence

  z=±2.58
• formula

  Margin of error formula

  
• Interval estimate is expressed as

  Lower limit (X-E<mean<X+E) Upper Limit
• Degrees of freedom (df)

  are the numbers of values that are free to vary after a sample statistics has been computed.
• Degrees of freedom formula

  df=n-1
• Margin of error formula when PSD are unknown

  E=t(s/√n)
• Interval estimate expression when sd is unknown

  (X-E˂µ˂X+E)
• T distribution

  Is a probability distribution that is used to estimate population parameters when the sample size is small and/or the population variance is unknown.
• T distribution

  Was developed by William Sealy Gosset in 1908
• Formula of t distribution

   $t=$$¯x−μ/s/√n$
• When will we use the formula of t distribution?

  When n<30 and the population standard deviation is unknown
• Properties of t distribution

  • Is symmetrical about 0
  • Is bell shaped like normal distribution but with heavier tails
  • The mean, median, and mode is equal to 0
  • The variance is always greater to 1. It is equal to v/v-2 where v is the number of degree of freedom
  • As the df increase, the curve looks more and more like the normal distribution
  • The standard deviation of t distribution varies with the sample size
  • The total area under at t distribution curve is 1 or 100%
• Formula of variance

  V/v-2

  Where v is df