Confidence levels, significance levels and critical values

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Intros
Lessons
  1. Using sample data, it is possible to find a Z-score relating to the claim (the test-statistic).

    Significance level

    Confidence Level (1α(1-\alpha)

    Significance Level (α\alpha)

    Critical Value (ZαZ_{\alpha})

    0.90

    0.10

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    0.95

    0.05

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    0.99

    0.01

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    Left Tail Test:

    . Left tail test, confidence levels, significance levels and critical values

    Right Tail Test:

    . Right tail test, confidence levels, significance levels and critical values

    Two tailed Test:

    . Two tail test, confidence levels, significance levels and critical values

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Examples
Lessons
  1. Finding the Critical Value
    With a significance level of α=0.075\alpha =0.075 what is the resulting critical value of:
    1. A right-tailed test?
    2. A left-tailed test?
    3. A two-tailed test?
  2. Find the critical value from the following confidence levels for a right-tailed test:
    1. 90% confidence
    2. 95% confidence
    3. 99% confidence
  3. Rejecting or Failing to Reject the Null Hypothesis
    The following Null Hypothesis and Alternative Hypothesis have been derived from a statement:

    H0H_0:
    p0.5p \leq 0.5

    H1H_1:
    pp > 0.5 0.5

    Using a significance level of 0.100.10 (which corresponds to a critical value of Zα=1.28Z_\alpha=1.28), and a Z-score of Z=1.40Z=1.40 relating to our Null Hypothesis;

    Can we reject the Null Hypothesis?
    1. The following Null Hypothesis and Alternative Hypothesis have been derived from a statement:

      H0H_0:
      μ175lbs\mu \geq 175 lbs

      H1H_1:
      μ\mu < 175lbs 175 lbs

      Using a 95% confidence level and a Z-score of Z=-1.50 relating to our Null Hypothesis;

      Can we reject the Null Hypothesis?
      1. The following claim is made.

        "70% of Canadians own a pet".

        Given that the test-statistic is Z=2.75, with a confidence level of 90% what can be said about the proportions of pet owners in Canada?