recitation10 - z table. If the test statistic is larger...

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Review and Examples The hypotheses for a hypothesis test take one of the following 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 The form chosen depends on the problem being asked. μ 0 is just a number. The hypotheses are statements about the parameter ( μ ) not the statistic x ). The equality is always in H 0 . After collecting data, we can decide to either: i. Reject H 0 and say that H a is true or ii. Do not reject H 0 and say that either H 0 or H a is true. Hypothesis Tests 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 z when we know the value of σ . z = ¯ x - μ 0 σ/ n 4. Form a conclusion. You can form a conclusion using two approaches: (a) The p -value approach. Use the z table to compute the p -value. If the p -value is less than α , reject H 0 . 1
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(b) The critical value approach. Look up the critical value on the
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Unformatted text preview: z table. If the test statistic is larger (either positively or negatively) than the critical value, reject H . Example : A production line is supposed to operate with a mean lling weight of 16 ounces per container. Overlling or underlling presents a serious prob-lem and when detected requires the operator to shut down the production line to readjust the lling mechanism. a. What are the hypotheses to be tested? b. If H is rejected, what course of action is required? Example : For the previous example, suppose a sample of 50 containers is taken. The sample average weight for the containers was 15.9 ounces. Past data suggests that = 1 . 0 ounces. Test the hypotheses from the previous example. Use = 0 . 05. 2...
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This note was uploaded on 01/24/2011 for the course STATISTICS 19897 taught by Professor Jager,abigaill during the Fall '10 term at Kansas State University.

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recitation10 - z table. If the test statistic is larger...

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