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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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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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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What is the relationship between the significance level of a test and Type I error?
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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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Defi ne Type I and Type II errors.
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Defi ne the term signifi cance level.
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Describe what the null and alternative hypotheses typically represent in the hypothesis-testing process.
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Formulate null and alternative hypotheses to test whether the mean annual snowfall in Buffalo, New York, exceeds 45 inches.
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Martha Inman, a highway safety engineer, decides to test the load-bearing capacity of a bridge that is 20 years old. Considerable data are available from similar tests on the same type of bridge. Which is appropriate, a one-tailed or a two-tailed test? If the minimum load-bearing capacity of this bridge must be 10 tons, what are the null and alternative hypotheses?
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Minhajur Rahaman
