Chapter+9

Sitisdifficulttocontrolfortheprobabilityofmaking

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Unformatted text preview: dical emergency requests Type I Error Because hypothesis tests are based on sample data, we must allow for the possibility of errors. s A Type I error is rejecting H0 when it is true. s The probability of making a Type I error when the null hypothesis is true as an equality is called the level of significance. s Applications of hypothesis testing that only control the Type I error are often called significance tests. Type II Error Type II Error s A Type II error is accepting H0 when it is false. s It is difficult to control for the probability of making a Type II error. s Statisticians avoid the risk of making a Type II error by using “do not reject H0” and not “accept H0”. Type I and Type II Errors Type I and Type II Errors Population Condition Conclusion H0 True (µ < 12) H0 False (µ > 12) Accept H0 (Conclude µ < 12) Correct Decision Type II Error Type I Error Correct Decision Reject H0 (Conclude µ > 12) p­Value Approach to One­Tailed Hypothesis Testing The p­value is the probability, computed using the test statistic, that measures the support (or lack of support) provided by the sample for the null hypothesis. If the p­value is less than or equal to the level of significance α, the value of the test statistic is in the rejection region. Reject H0 if the p­value < α . Lower­Tailed Test About a Population Mean: σ Known • p­Value Approach p­Value < α , so reject H0. α = .10 Sampling distribution x − µ0 z of = σ/ n p­value = .0 7 2 z z = ­zα = ­1.46 ­1.28 0 Upper­Tailed Test About a Population Mean: σ Known • p­Value Approach p­Value < α , so reject H0. Sampling distribution x − µ0 z of = σ/ n α = .04 p­Value = .0 1 1 z 0 zα = 1.75 z = 2.29 Critical Value Approach to Critical Value Approach to One­Tailed Hypothesis Testing The test statistic z has a standard normal probability distribution. We can use the standard normal probability distribution table to find the z­value with an area of α in the lower (or upper) tail of the distribution. The value of the test statistic that established the boundary of the rejection region is called the critical value for the test. s The rejection rule is: • Lower tail: Reject H0 if z < ­zα • Upper tail: Reject H0 if z > zα Lower­Tailed Test About a Population Mean: σ Known • Critical Value Approach Sampling distribution x − µ0 z= of σ/ n Reject H0 α = .1 0 − α = − z 1.28 Do Not Reject H0 0 z Upper­Tailed Test About a Population Mean: σ Known • Critical Value Approach Sampling distribution x − µ0 z of = σ/ n Reject H0 Do Not Reject H0 0 α = .0 5 zα = 1.645 z Steps of Hypothesis Testing Steps of Hypothesis Testing Step 1. Develop the null and alternative hypotheses. Step 2. Specify the level of significance α. Step 3. Collect the sample data and compute the test statistic. p­Value Approach Step 4. Use the value of the test statistic to compute the p­value. Step 5. Reject H0 if p­value < α. Steps of Hypothesis Tes...
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