STATISTICS

• Sampling Distribution of Sample Means


  A frequency distribution using the means computed from all possible random samples of a specific size taken from a population
• Sampling Error


  The difference of the sample mean and the population
• Steps in Constructing the Sampling Distribution of the Means


  1. Determine the number of sets of all possible random samples that can be drawn from the given population

  2. List all the possible samples and compute the mean of each sample

  3. Construct the sampling distribution

  
• Estimate


  The value or range values that approximates the population value
• Estimation


  The process of determining parameter values
• Mean


  Also known as the average computed from the table
• Parameter


  The number that describes the population
• Statistic


  The number that describes the sample
• Point Estimate


  A specific numerical value of population parameter, best estimate of a population mean
• Interval Estimate


  Range of values used to estimate parameters, the estimate may or may not contain the true parameter values
• 3 Types of Estimation

  • Unbiased
  • Negative Bias
  • Positive Bias
• Critical Values/Confidence Coefficients


  The z-values used in describing the characteristics of a target population, used when population standard deviation is known
• Confidence Levels and Corresponding Z-Values

  • 90% Confidence: z = ± 1.65
  • 95% Confidence: z = ± 1.96
  • 99% Confidence: z = ± 2.58
• Margin of Error


  The maximum difference between the observed sample mean and the true value of the population mean
• Degrees of Freedom


  The numbers of values that are free to vary after a sample statistics has been computed
• Central Limit Theorem (CLT)


  States that sampling distribution of the sample means moves closer to normal distribution as the sample size increases regardless of the shape of the population distribution, also tells us that the mean of the sampling distribution of the sample means is always equal to the population mean
• Assumptions and Conditions for Using the CLT

  • The sample must be selected randomly
  • The variables must be independent from each other
  • The sample size should not be more than 10% or less of the population when the sample is drawn with no replacement
  • The sample size must be large enough (minimum sample size of 30)
• The Central Limit Theorem gives us confidence that whatever the shape of the distribution is, it will approach a normal distribution as the sample size increases
• Formula used to determine the number of sets of all possible random samples that can be drawn from the given population

  A) N!

  B) n!(N-n)!

  
• Margin of error formula

  A) sample size

  B) sample standard deviation

  C) z-value

  
• Degrees of freedom$DF=$$n-1$

  n = sample size
• Margin of error formula using degrees of freedom

  where;

  • E: margin of error
  • t: degrees of freedom
  • s: sample standard deviation
  • n: sample size

  A) t

  B) s

  C)

  
• Interval Estimate: A range of values that is estimated to be between two other values.