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recitation11 - Review and Examples Hypothesis Tests for...

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Review and Examples Hypothesis Tests for means (with unknown σ ) consist of four steps: 1. State the hypotheses. The hypotheses should take one of these forms: H 0 : μ μ 0 H a : μ < μ 0 H 0 : μ μ 0 H a : μ > μ 0 H 0 : μ = μ 0 H a : μ 6 = μ 0 2. State the level of significance. This is denoted with α . 3. Compute the test statistic. We use the test statistic t when we do not know the value of σ . t = ¯ x - μ 0 s/ n 4. Form a conclusion. You can form a conclusion using two approaches. Remember the degrees of freedom is n - 1. (a) The p -value approach. Use the t table to compute the p -value. If the p -value is less than α , reject H 0 . (b) The critical value approach. Look up the critical value on the t table. If the test statistic is larger (either positively or negatively) than the critical value, reject H 0 . Example (Using Excel to do Hypothesis Tests) : The U.S. Energy Adminis- tration reported that the mean price for a gallon regular gasoline in the United States was $2.36. We want to determine if gasoline prices in the Lower Atlantic states are lower than the national average.
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