STATS

• Hypothesis testing is a method of using sample data to decide between two competing claims

  (hypotheses) about a population.
• statistical hypothesis is a prediction regarding the possible outcome of a study. It can be shown to be supported or not supported.
• null hypothesis, denoted by Ho, is the hypothesis to be tested. It has a statement of equality, such

  as ≥, ≤ or =.
• alternative hypothesis, denoted by Ha, is the hypothesis that has no statement of equality, such as >, < or ≠.
• One-tailed test makes use of only one side or tail of the statistical model or distribution.
• Right-tailed test: It is used when an assertion is made that the difference falls within the positive

  end of the distribution. The alternative hypothesis uses comparatives such as greater than,

  higher than, better than, superior to, exceeds, above, increased, etc.
• Left-tailed test: It is used when an assertion is made that the difference falls within the negative

  end of the distribution. The alternative hypothesis uses comparatives such as less than, smaller

  than, inferior to, lower than, below, decreased, etc.
• Two-tailed test, makes use of two opposite sides or tails of the statistical model or distribution. It is

  used when no assertion is made as to whether the difference falls within the positive or the negative

  end of the distribution. The alternative hypothesis uses comparatives such as not equal to, different

  from, not the same as, etc.
• TYPES OF HYPOTHESIS TESTING:

  1. One-tailed test
  2. Two-tailed test
• Level of significance, denoted by α (alpha), is the probability of rejecting the null hypothesis in favor

  of the alternative hypothesis when it is really true.
• The rejection region pertains to the set of all values for which the null hypothesis will be rejected.
• Type I error occurs when the null hypothesis is rejected when it is true. This means that a true

  hypothesis is incorrectly rejected.
• Type II error occurs when the null hypothesis is not rejected when it is false. This means that a false

  hypothesis is incorrectly accepted.
• The z-test is used when the population variance 𝜎

  2

  is known and either the distribution is normal or the

  sample size n is sufficiently large, that is n≥ 30.
• The t-test is used when the population variance 𝜎

  2

  is unknown and the sample size is not sufficiently

  large (n<30).
• A proportion represents a part of a whole. It can be expressed as a fraction, decimal, or percentage.
• population proportion, denoted by , refers to a fractional part of a population possessing certain

  characteristics. It can take on any value from 0 to 1.
• Central Limit Theorem for Proportion states that the sampling distribution of the sample

  proportion 𝑝̂(read: “p hat”) is approximately normally distributed with mean and standard deviation √

  𝑝𝑞

  𝑛

  if the sample size n is sufficiently large but no more than 5% of the population size, where is the

  population proportion and q=1-p.
• The range of values that leads the researcher to reject the null

  hypothesis and choose the alternative hypothesis is called the rejection region.