STATS

• Hypothesis Testing

  ▪ It is a decision-making process for evaluating claims

  about a population.

  ▪It is basically testing an assumption that we can make

  about a population.
• A hypothesis is an assumption or conjecture about a

  population parameter which may or may not be true.
• A parameter is any numerical quantity that

  characterizes a given population or some of its aspects.

  This means the parameter tells us something about the

  whole population.
• statistic is the numerical measure that s calculated from the sample
• statistic is a known number and a variable that depends on the portion of the population
• parameter = true value
• example of parameters are the measures of central tendency (mean median mode)
• basta e2

  
• •Null Hypothesis – denoted by Ho , is a

  statement saying that there is no

  difference between a parameter and a

  specific value.
• •ALTERNATIVE HYPOTHESIS – denoted by

  Ha , is the opposite or negation of the null

  hypothesis.
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• Null Hypothesis, Ho

  = equal to, the same as, not changed, is

  ≥ greater than or equal to, at least

  ≤ less than or equal to, at most
• Alternative Hypothesis, Ha or H1

  ≠ not equal, different from, changed from, not the same as

  > greater than, above, higher than, longer than, bigger

  than, increased

  < less than, below, lower than, smaller than, shorter than,

  decreased or reduced from
• TYPES OF TESTS

  ▪Directional test (one-tailed test)

  The rejection region is on one side of the

  distribution. It is either on the left or on the

  right tail of the curve depending on how the

  alternative hypothesis is tested.
• ▪Non-Directional test (two-tailed test)

  The rejection region is on both sides of the curve. If

  the alternative hypothesis contains inequality (≠)

  symbol , then the test is two-tailed.
• Rejecting the null hypothesis when it is true is called

  a Type I error with probability denoted by

  alpha (α). In hypothesis testing, the normal curve that

  shows the critical region is called the alpha region.
• Accepting the null hypothesis when it is false is called

  a Type II error with probability denoted by beta. In

  hypothesis testing, the normal curve that shows the

  acceptance region is called beta region.
• The larger the value of alpha, the smaller is the value of

  beta.
• ▪If the null hypothesis is true and

  accepted, or if it is false and rejected, the

  decision is correct.
• ▪If the null hypothesis is true and rejected,

  the decision is incorrect, and this is

  Type I error.
• ▪If the null hypothesis is false and

  accepted, the decision is incorrect, and

  this is a Type II error.
• In the figure, the level of significance is

  represented by Greek symbol α (alpha). It is a

  small area at the tail end of the normal curve which

  defines the rejection region (critical region)
• The level of significance tends to regulate

  outcomes that may lead to commit a type I

  error.
• These outcomes may be caused by

  samples occupying the extreme areas (with the

  lower or highest scores)
• The usual probability values of a type I error

  used are 10%, 5% or 1%
• Z-test, if population standard deviation is

  known and n ≥ 30
• T-test, if population standard deviation is

  unknown and n < 30