SECTION 7.2 Hypothesis Testing for the Mean (s Known) 365 Using P@Values for a z-Test You will now learn how to perform a hypothesis test for a mean m assuming the standard deviation s is known. When s is known, you can use a z@test for the mean. To use the z@test, you need to find the standardized value for the test statistic x. The standardized test statistic takes the form of z = 1Sample mean2 - 1Hypothesized mean2 Standard error . The z@test for a mean M is a statistical test for a population mean. The test statistic is the sample mean x. The standardized test statistic is z = x - m s 1n Standardized test statistic for m (s known) when these conditions are met. 1. The sample is random. 2. At least one of the following is true: The population is normally distributed or n Ú 30. Recall that s 1n is the standard error of the mean, sx. z-Test for a Mean M Using P@Values for a z@Test for a Mean M (S Known) In Words In Symbols 1. Verify that s is known, the sample is random, and either the population is normally distributed or n Ú 30. 2. State the claim mathematically State H0 and Ha. and verbally. Identify the null and alternative hypotheses. 3. Specify the level of significance. Identify a. 4. Find the standardized test statistic. z = x - m s 1n 5. Find the area that corresponds to z. Use Table 4 in Appendix B. 6. Find the P@value. a. For a left-tailed test, P = 1Area in left tail2. b. For a right-tailed test, P = 1Area in right tail2. c. For a two-tailed test, P = 21Area in tail of standardized test statistic2. 7. Make a decision to reject or fail If P … a, then reject H0. to reject the null hypothesis. Otherwise, fail to reject H0. 8. Interpret the decision in the context of the original claim. GUIDELINES With all hypothesis tests, it is helpful to sketch the sampling distribution. Your sketch should include the standardized test statistic.
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