STATS-L2

• Hypothesis


  A statement of belief used in the evaluation of population values
• Hypothesis


  Assumption, scientific or educated guess, prediction
• Hypothesis testing


  A statistical procedure of drawing conclusion that generally pertains to the characteristic/s of population through sample data
• Steps in hypothesis testing


  1. Formulation of Null and Alternative Hypotheses

  2. Select the Level of Significance (α)

  3. Determine the Test of Statistics to Use

  4. Define the Area of Rejection or the Critical Region

  5. Compute for the value of the statistical test

  6. Decision

  7. Interpretation or Conclusion
• Null hypothesis (H0)


  • Refers to any claim or assertion pertaining to the parameter of the population
  • The hypothesis that is intended to reject in conducting hypothesis testing
  • It is known as the "NULL hypothesis" because of insufficient or absence of statistical evidences or facts to warrant its truthfulness
  • Always a statement of equality
• Alternative hypothesis (Ha)


  • An assertion or claim that disagrees or contradicts the null hypothesis
  • Always a statement of inequality
• Symbols used in hypothesis

  • <<>Less than
  • ≤>Less than or equal to
  • >Greater than
  • ≥>Greater than or equal to
• Formulating H0 and Ha (Form I)

  • H0: The average monthly income in a certain barangay is equal to P15,000 (μ = 15,000)

  Ha: The average monthly income in a certain barangay is higher than P15,000 (μ > 15,000)
• Formulating H0 and Ha (Form II)

  • H0: The average IQ of students is equal to 75% (μ = 75%)

  Ha: The average IQ of students is lower than 75% (μ < 75%)
• Formulating H0 and Ha (Form III)

  • H0: The mean IQ of students is higher or equal to 75% (μ ≥ 75%)

  Ha: The mean IQ of students is lower than 75% (μ < 75%)
• Formulating H0 and Ha (Form IV)


  • H0: The average monthly income of Nurses in NCR is not higher than ₱25,000 (μ ≤ 25,000)

  Ha: The average monthly income of Nurses in NCR is higher than ₱25,000 (μ > 25,000)
• Formulating H0 and Ha (Form V)


  • H0: The average monthly salary of employees of company A and B are the same (μA = μB)

  Ha: The average monthly salary of employees of company A and B are not the same (μA ≠ μB)
• Level of Significance (α)


  It corresponds to the area in the critical region

  It is the degree of significance in which we reject or recognize the H0

  When a test statistic fall or included with this area, the result is referred to as significant level α

  Measures the "risk" associated with making an error
• Level of Confidence (1-α)


  Degree of assurance (belief) that a particular statistical statement is correct under specified conditions
• Level of Significance (α)

  Degree of uncertainty (doubt) about the statistical statement under the same conditions used to determine the confidence level
• Calculating Level of Significance (α)


  • If Level of Confidence (1-α) = 97%, then α = 1 - 0.97 = 0.03 or 3% level of significance
• The teacher claims that the average grade of SHS students enrolled in Statistics class is higher than 85 with a standard deviation of 7.8. A random sample of 250 students are selected and found out that their mean is 81. The teacher is 95% confident in his claim. The level of significance (α) is 0.05
• Parametric Test


  Requires normal distribution

  Levels of measurement are expressed in an interval or ratio

  More powerful than nonparametric test
• Parametric Tests


  • z-test

  1. test

  Paired t-test

  Analysis of Variance (ANOVA)
• Non-Parametric Test


  Used when the given data is qualitative and usually measured in terms of ordinal or nominal

  Used when researchers doubt the validity of the parametric test
• Non-Parametric Tests


  • Sign Test

  Wilcoxon signed-rank test

  Wilcoxon rank-sum test

  Kruskal-Wallis test

  Chi-square test
• 1. test


  Used for testing hypothesis when the population standard deviation is known and the sample size is at least 30
• 1. test


  Used for testing hypothesis when the sample standard deviation, s, is known and the sample size is less than 30
• Rejection Region


  The region at far end of the distribution

  Also known as the Critical Region

  It is the area under the normal curve in which null hypothesis is rejected based on the set condition (decision rule)

  Denoted by α
• Critical value or Tabulated value (TV)

  Separates the area of rejection and the area in which null hypothesis is not rejected under the normal curve
• Type I Error


  Committed when the null hypothesis is true but decided to go in contradiction

  Denoted by α
• Type II Error


  Committed when the researcher decided to favor a null hypothesis that is actually false

  Denoted by β
• In a two-tailed test, the null hypothesis is rejected if the test statistic falls in the critical region on either side of the distribution
• In a one-tailed test, the null hypothesis is rejected if the test statistic falls in the critical region on one side of the distribution
• Rules to follow in hypothesis testing

  State the appropriate conclusion in the context of the problem and the level of significance used
• Reject Ho


  If the test statistic falls in the critical region
• Do not reject Ho


  If the test statistic falls in the non-rejection region
• Type I Error - committed when the null hypothesis is true but decided to go in contradiction. Denoted by α.
• Type II Error - committed when the researcher decided to favor a null hypothesis that is actually false. Denoted by β.
• Two-tailed test


  • Ha is ≠
• One-tailed test


  • Ha is either < or >
• Interpretation or Conclusion


  State the appropriate conclusion. In addition, the conclusion should be affirmed in the context of the problem and the level of significance.
• Example conclusion


  • Based on the computed value of _______ equals to ___ which is _____ the tabulated value of ____, using ___ level of significance, hence ______ Ho. Therefore, ____________________________________________ . This further implies that the claim is _______.
• Hypothesis Testing


  Process of determining whether a hypothesis about a population parameter is likely to be true or false
• Null hypothesis (Ho): The claim that is being tested