Key Concepts

• If the alternative hypothesis contains > or <, then the test is called a one-sided test.  If the alternative hypothesis contains ≠, then the test is called a two-sided test.
• The basic steps to doing a hypothesis test are:
  • Determine what procedure should be done.
  • State the null and alternative hypotheses.
  • Check that the conditions for doing the procedure have been met.
  • Calculate the test statistic and p-value.
  • Make a conclusion based on an [latex]\alpha[/latex] level.
  • State your conclusion in the context of the problem.

Glossary

Hypothesis: a statement about the value of a population parameter. In case of two hypotheses, the statement assumed to be true is called the null hypothesis (notation [latex]H_0[/latex]) and the contradictory statement is called the alternative hypothesis (notation [latex]H_a[/latex]).

Hypothesis Testing: based on sample evidence, a procedure for determining whether the hypothesis stated is a reasonable statement and should not be rejected, or is unreasonable and should be rejected.

Level of Significance of the Test: probability of a Type I error (reject the null hypothesis when it is true). Notation: [latex]\alpha[/latex]. In hypothesis testing, the Level of Significance is called the preconceived [latex]\alpha[/latex] or the preset [latex]\alpha[/latex].

p-value: the probability that an event will happen purely by chance assuming the null hypothesis is true. The smaller the p-value, the stronger the evidence is against the null hypothesis.