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Hypothesis Testing of Single Mean and Single Proportion: Summary of Formulas

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

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HoHo and HaHa are contradictory.

Table 1
If HoHo has: equal (=)(=) greater than or equal to ()() less than or equal to ()()
then HaHa has: not equal (≠)(≠) or greater than (>)(>) or less than (<)(<) less than (<)(<) greater than (>)(>)

If α α p-value, then do not reject H o H o.

If α > α> p-value, then reject H o H o .

αα is preconceived. Its value is set before the hypothesis test starts. The p-value is calculated from the data.

αα = probability of a Type I error = P(Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true.

ββ = probability of a Type II error = P(Type II error) = probability of not rejecting the null hypothesis when the null hypothesis is false.

If there is no given preconceived αα, then use α=0.05α=0.05.

Types of Hypothesis Tests

  • Single population mean, known population variance (or standard deviation): Normal test.
  • Single population mean, unknown population variance (or standard deviation): Student-t test.
  • Single population proportion: Normal test.

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