Hypothesis Testing

• Hypothesis testing is a statistical method applied in making decisions using experimental data. Hypothesis testing is basically testing an assumption that we make about a population.
• Hypothesis


  A proposed explanation, assertion, or assumption about a population parameter or about the distribution of a random variable
• Null hypothesis (Ho)


  An initial claim based on previous analyses, which the researcher tries to disprove, reject, or nullify. It shows no significant difference between two parameters.
• Alternative hypothesis (Ha)


  Contrary to the null hypothesis, which shows that observations are the result of a real effect.
• The level of significance denoted by alpha or α refers to the degree of significance in which we accept or reject the null hypothesis.
• 1. z test

  • It can be used when the sample is large, that is n ≥ 30
  • It is also called z statistic
  • The z statistic measures the number of standards between the observed value of and the null hypothesized value of µ
• 100% accuracy is not possible in accepting or rejecting a hypothesis. The significance level α is also the probability of making the wrong decision when the null hypothesis is true.
• The commonly used levels of significance are 0.01, 0.05 and 0.10.
• Directional Test (one-tailed)


  A test of any statistical hypothesis where the alternative hypothesis is expressed using less than (<) or greater than (>).
• Non-Directional Test (Two-tailed)


  A test of any statistical hypothesis where the alternative hypothesis is written with a not equal sign (≠).
• Steps in Hypothesis Testing

  1. Identify the claim and formulate the null and alternative hypothesis

  2. Identify the type of test (one-tailed or two-tailed), critical value at a specified level of significance, rejection region

  3. Compute the test value, using the test statistic or formula for the test

  4. Make a decision whether to accept or reject the null hypothesis

  5. Make a conclusion by answering the research question
• If Ho is rejected at 0.05 level, then it is usually labeled as "significant", otherwise the result is labeled "not significant". If Ho is rejected at 0.01 level, then the result is labeled "Highly significant".
• Type I Error


  Occurs when the null hypothesis is true and rejected, the decision is incorrect. It is also called alpha error (α error).
• Null Hypothesis (Ho)


  The average capacity of a particular bottled fruit juice that the factory sells is 250 ml
• Alternative Hypothesis (Ha)


  The average capacity of a particular bottled fruit juice that the factory sells is not equal to 250 ml
• Null Hypothesis (Ho)


  The average weight reduced to overweight women by a new drug on the market is less than or equal to 4.55 kg. per month
• Alternative Hypothesis (Ha)


  The average weight reduced to overweight women by a new drug on the market is greater than 4.55 kg. per month
• Null Hypothesis (Ho)


  The average diameter of the skull of a primitive man is more than 7 inches
• Alternative Hypothesis (Ha)


  The average diameter of the skull of a primitive man is not more than 7 inches
• Null Hypothesis (Ho)


  The average sentence of perpetrators of a crime who have been given the maximum sentence of 10 years is no more than 7 years
• Alternative Hypothesis (Ha)


  The average sentence of perpetrators of a crime who have been given the maximum sentence of 10 years is more than 7 years
• Null Hypothesis (Ho)


  The proportion of all purchasers of a certain kind of computer program will call the manufacturer's hotline within one month purchase is Equal to 60%
• Alternative Hypothesis (Ha)


  The proportion of all purchasers of a certain kind of computer program will call the manufacturer's hotline within one month purchase is less than 60%
• Null Hypothesis (Ho)


  The proportion of all patients exposed to a certain amounts of radiation will feel ill effects is equal to 10%
• Alternative Hypothesis (Ha)


  The proportion of all patients exposed to a certain amounts of radiation will feel ill effects is not equal to 10%
• Null Hypothesis (Ho)


  The proportion of academic students is equal to the proportion of TVL students
• Alternative Hypothesis (Ha)


  The proportion of academic students is not equal to the proportion of TVL students
• Hypothesis testing is a statistical method applied in making decisions using experimental data.
• Hypothesis testing is testing an assumption that we make about a population.
• Hypothesis is a proposed explanation, assertion, or assumption about a population parameter or about the distribution of a random variable
• Null hypothesis is an initial claim based on previous analyses, which the researcher tries to disprove, reject, or nullify. It shows no significant difference between two parameters. It is denoted by 𝐻𝑜.
• Alternative hypothesis is contrary to the null hypothesis, which shows that observations are the result of a real effect. It is denoted by 𝐻𝑎.
• Type I Error – Occurs when the null hypothesis is rejected even though it is actually true.
• Type I Error occurs when the null hypothesis is rejected even though it is true.
• Type II Error occurs when the null hypothesis is accepted even though it is false.
• Type II error - Occurs when the null hypothesis is not rejected although it is false.
• The level of significance denoted by alpha or 𝛂 refers to the degree of significance in which we accept or reject the null hypothesis.
• The commonly used levels of significance are 0.01, 0.05 and 0.10
• 100% accuracy is not possible in accepting or rejecting a hypothesis
• Rejection region (or critical region) is the set of all values of the test statistic that causes us to reject the null hypothesis.