Significance Tests(KA/SAP/U12SignificanceTests)

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Unit 12: Significance Tests (Hypothesis Testing)

Topics Covered:
  • The idea of significance tests
  • Error probabilities and power
  • Tests about a population proportion
  • Tests about a population mean

The Idea of Significance Tests

Significance tests, also known as hypothesis tests, are statistical methods used to make decisions or inferences about population parameters based on sample data. The process involves:

  1. Stating a null hypothesis (H0) and an alternative hypothesis (Ha).
  2. Collecting and summarizing sample data.
  3. Calculating a test statistic and a p-value.
  4. Comparing the p-value to a significance level (α) to decide whether to reject H0.
Quiz:

Error Probabilities and Power

When conducting significance tests, two types of errors can occur:

  • Type I Error (α): Rejecting the null hypothesis when it is actually true.
  • Type II Error (β): Failing to reject the null hypothesis when the alternative is true.

Power of a test is the probability of correctly rejecting a false null hypothesis (1 - β).

Quiz:

Tests About a Population Proportion

Significance tests about a population proportion are used to determine if the proportion of a certain characteristic in a population is equal to a hypothesized value. The steps are:

  1. State hypotheses: H0: p = p0, Ha: p ≠ p0 (or <, >).
  2. Check conditions: Random, 10%, and Large Counts conditions.
  3. Calculate the test statistic:
    z = (p̂ - p₀) / √[p₀(1-p₀)/n]
  4. Find the p-value and make a conclusion.
Quiz:

Tests About a Population Mean

Significance tests about a population mean are used to determine if the mean of a population is equal to a hypothesized value. The steps are:

  1. State hypotheses: H0: μ = μ0, Ha: μ ≠ μ0 (or <, >).
  2. Check conditions: Random, 10%, and Normal/Large Sample conditions.
  3. Calculate the test statistic:
    t = (x̄ - μ₀) / (s/√n)
  4. Find the p-value and make a conclusion.
Quiz:

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