Statistics and Probability

• Parameters - descriptive measure of an entire population however their values are usually unknown

  • it's not feasible to measure an entire population and because of this a sample from the population is taken to obtain parameter estimates
• Sample Statics - estimate of the population parameters along with the amount of error associated with these estimates
• Estimation - Process of estimating or approximately calculating the value of a parameter from information drawn from the samples

  • the object of estimation is to determine the approximate value of population parameter based on the basis of sample statistics
  • one aspect of inferential statistics because we get approximate values from the population parameter from the information drawn from a sample
• Estimator - the estimator of the population parameter is the sample statistics

  -attempts to approximate the unknown parameter using measurements
• Estimate - the computed sample statistics
• Point Estimates - single most likely value of a sample statistic that is used to estimate a population parameter
• Properties of Desirable Estimator:

  • Unbiased - happens when the mean or expectation of the statistic is equal to the parameter
  • Consistent - the difference between the estimator and the parameter becomes smaller as the sample size grows bigger
  • Relatively Efficient - if there are two unbiased estimators of a parameter, the one whose variance is smaller should be used
• Interval Estimates - or confidence Intervals are a range of values to estimate a parameter

  • a degree confidence, ususally a percent, can be assigned before an interval estimate is used
  • confidence lies with some region with some prescribed probability
  • confidence level is associated with a confidence interval which states how much confidence we have that the interval contains the true population parameter
  • the more frequent values for a confident interval are 99% , 95% . and 90% with corresponding margin of errors 1%, 5%, 10%
• Margin of Level - refers to the maximum acceptable difference ( determine by a) between the observed sample statistic and the true population parameter