Stats

• Hypothesis


  A proposed explanation, assertion, or assumption about a population parameter or the distribution of a random variable
• Type I error


  We reject a null hypothesis that is true
• Parameter


  The average age of 10 college students is 24 years
• Parameter


  The percentage of teachers who would rather drink coffee than soft drinks during break time
• Null hypothesis (Ho)


  The average lifetime of the plant is 60 months
• Alternative hypothesis (Ha)


  The average lifetime of the plant is not 60 months
• 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.
• Null hypothesis (Ho)


  The 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.
• Hypothesis testing


  1. Reject the null hypothesis

  2. Fail to reject null hypothesis
• Level of significance (α)

  The degree of significance in which we accept or reject the null hypothesis. It is the probability of making the wrong decision when the null hypothesis is true.
• Level of confidence (c)

  The most common levels are 90%, 95%, 99%. It is the complement of the level of significance (α = 1 - c).
• Rey uses 5% level of significance in proving that there is no significant change in the average weight of energy bars in 10 machines that went through maintenance for the last 3 months.
• Level of confidence


  Represented by c, common levels are 90%, 95%, 99%
• Level of significance


  Represented by alpha (∝), the complement of the level of confidence (∝ = 1 - c)
• The complement of the level of confidence is the level of significance
• Two-tailed test


  • Used when the alternative hypothesis (Ha) contains the symbol ≠
• One-tailed test


  • Used when the alternative hypothesis (Ha) contains the symbol < or >
• Rejection region


  The set of all values of the test statistic that causes us to reject the null hypothesis
• Non-rejection region


  The set of all values of the test statistic that causes us to fail to reject the null hypothesis
• Critical value


  A point (boundary) on the test distribution that is compared to the test statistic to determine if the null hypothesis would be rejected
• Type I error


  Rejecting the null hypothesis when it is true, with probability denoted by alpha (∝)
• Type II error


  Accepting the null hypothesis when it is false, with probability denoted by beta (β)
• Parameter


  Any numerical quantity that characterizes a given population or some of its aspects
• Statistic


  The numerical measure that is calculated from the sample
• Null hypothesis (H0)


  Always has an = symbol
• Alternative hypothesis (Ha)


  Never has an = symbol
• Null and alternative hypotheses

  • H0: μ = k
  • H0: μ ≤ k
  • H0: μ ≥ k

  Ha: μ ≠ k

  • Ha: μ > k
  • Ha: μ < k