Stats

• population parameter


  A numerical characteristic of a population
• HYPOTHESIS


  A claim or assumption about the value of a population parameter
• HYPOTHESIS TESTING


  A method for testing a claim or assumption about a population parameter
• TWO WAYS to STATE HYPOTHESIS

  • Null hypothesis (Ho) - Statement about the population parameter that is assumed to be true
  • Alternative hypothesis (Ha) - Statement that directly contradicts the Ho by stating the actual value of the population parameter is less than, greater than, or not equal to the value stated in the Ho
• Examples


  • Ho: The average age of a bus driver in Manila is 35.8 years

  Ha: The average age of a bus driver in Manila is not 35.8 years

  Ho: The average number of calories of a low calorie meal is at most 300

  Ha: The average number of calories of a low calorie meal is more than 300

  Ho: The mean score of incoming Grade 11 is 81

  Ha: The mean score of incoming Grade 11 is not 81

  Ho: A new medicine reduces uric acid by 50%

  Ha: The new medicine does not reduce uric acid by 50%
• Level of Significance


  Denoted as alpha, it is the pre-determined probability of rejecting the Ho when it is true (Type I error)
• Common levels of significance are 1%, 5%, and 10%
• Type I Error


  Rejecting the Ho when it is true
• Type II Error


  Failing to reject the Ho when it is false
• The probability of committing a Type I error is alpha, while the probability of committing a Type II error is beta
• Rejection Region


  The range of values of the test statistic where the Ho is rejected in favor of the Ha
• Region of Acceptance


  The range of values of the test statistic where the Ho is not rejected
• Parameters that can be tested

  • Mean
  • Variance
  • Standard Deviation
  • Proportion
• Computed Value (Zc or Tc)

  The test statistic calculated from the sample data
• Critical Value (Zα or Tα)


  The value of the test statistic that determines the boundary between the rejection and acceptance regions
• Steps in Hypothesis Testing


  State the null and alternative hypotheses

  2. Determine the statistical technique and level of significance

  3. Establish the critical value and the decision rule

  4. Compute the test statistic

  5. State the decision and conclusion