Describe what the null and alternative hypotheses typically represent in the hypothesis-testing process.
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Defi ne the term signifi cance level.
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Defi ne Type I and Type II errors.
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In a trial, the null hypothesis is that an individual is innocent of a certain crime. Would the legal system prefer to commit a Type I or a Type II error with this hypothesis?
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What is the relationship between the significance level of a test and Type I error?
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If our goal is to accept a null hypothesis that μ = 36.5 with 96 percent certainty when it’s true, and our sample size is 50, diagram the acceptance and rejection regions for the following alternative hypotheses: (a) μ ≠ 36.5. (b) μ > 36.5. (c) μ < 36.5
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For the following cases, specify which probability distribution, to use in a hypothesis test: (a) H 0: μ = 15, H1: μ ≠ 15, x = 14.8, ˆσ = 3.0, n = 35. (b) H 0: μ = 9.9, H1: μ ≠ 9.9, x = 10.6, σ = 2.3, n = 16. (c) H 0: μ = 42, H1: μ > 42, x = 44, σ = 4.0, n = 10. (d) H0: μ = 148, H1: μ > 148, x = 152, ˆσ = 16.4, n = 29. (e) H 0: μ = 8.6, H1: μ < 8.6, x = 8.5, ˆ σ = 0.15, n = 24.
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Your null hypothesis is that the battery for a heart pacemaker has an average life of 300 days, with the alternative hypothesis being that the battery life is more than 300 days. You are the quality control engineer for the battery manufacturer. (a) Would you rather make a Type I or a Type II error? (b) Based on your answer to part (a), should you use a high or a low significance level?.
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Under what conditions is it appropriate to use a one-tailed test? A two-tailed test?.
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If you have decided that a one-tailed test is the appropriate test to use, how do you decide whether it should be a lower-tailed test or an uppertailed test?
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