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H o and H a are contradictory.

If H o has: equal (=) greater than or equal to ( ) less than or equal to ( )
then H a has: not equal (≠) or greater than ( > ) or less than ( < ) less than ( < ) greater than ( > )

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

If α > p-value, then reject H o .

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

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

β = 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 α , then use α = 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's-t test .
  • Single population proportion: Normal test .

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Source:  OpenStax, Elementary statistics. OpenStax CNX. Dec 30, 2013 Download for free at http://cnx.org/content/col10966/1.4
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