STATS (Lesson 1)

• What is Hypothesis Testing?

  • Is a decision-making process of evaluating claims about a population based on the characteristics of a sample from that population. It decides whether to reject or accept the null hypothesis.
• • Null hypothesis is a statement denoted by Ho, that states that there is no difference, no changes, nothing happened, no relationship between a parameter and a specific value, or the independent variable has no effect on the dependent variable.
• Null is defined as having no value or amounting to nothing
• Ho - Null Hypothesis

  μ - Population Parameter

  = - Equality Symbol

  100 - Value of the population parameter
• Example of Null Hypothesis is "There is no significant difference between the average hourly rate for construction workers and the average hourly rate for manufacturing workers."
• Alternative hypothesis, a statement denoted by H1, is a statement that states that there is a difference, and effect, change, or a relationship between a parameter and a specific value; the independent variable has an effect on the dependent variable, or something happened.
• • An alternative hypothesis is a statement that directly contradicts a null hypothesis by stating that that the actual value of a population parameter is less than, greater than, or not equal to the value stated in the null hypothesis.
• In symbol, it is written as:

  Η ₁: μ ≠ 100

  Η ₁: μ < 100 

  Η₁: μ > 100
• The alternative hypothesis will also determine the type of hypothesis test that will be conducted.

  One-tailed test will be used when using > or <.

  Two-tailed test will be used when ≠ is used
• >

  greater than

  above

  higher than

  longer than

  bigger than

  increased
• <

  • less than
  • below
  • lower than
  • smaller than
  • shorter than
  • decreased or reduced from
• ≠

  not equal

  different from

  changed from

  not the same as
• =

  equal to

  the same as

  not changed from

  is
• Level of significance, or significance level, refers to a criterion of judgment upon which a decision is made regarding the value stated in a null hypothesis. Its value is between 0 to 1 or between 0% to 100%.
• if the alternative hypothesis used is ≠ (not equal to), then the alpha will be divided by two:
• CRITICAL REGION, also known as rejection region, is a range of values that corresponds to the rejection of the null hypothesis. If the value of the test statistics is within the critical region, then the null hypothesis is rejected. Otherwise, the null hypothesis is not rejected. This will be based on the alternative hypothesis.
• For one-tailed test or directional test < (less than), the critical region is at the left side of the acceptance region.

  For one-tailed test or directional test > (greater than), the critical region is at the right side of the acceptance region.

  For two-tailed test or non-directional test ≠, the critical region is at the left and right sides of the acceptance region.
• Types of Error

  1. Type I error is committed when rejecting a true null hypothesis. The probability of committing it is denoted by a or the level of significance.

  2. Type II error is committed when accepting a false null hypothesis. The probability of committing it is denoted by ẞ
• • Type I error - We conclude that the mean number of years a teacher works before retiring is not 30 years, when it really is 30 years.
  • Type II error - We conclude that the mean number of years a teacher works before retiring is 30 years, when in fact it really is not 30 years.