Chapter+9

Forz247cumulativeprobability9932 pvalue1 99320068

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Unformatted text preview: ting Critical Value Approach Critical Value Approach Step 4. Use the level of significance to determine the to determine the critical value and the rejection rule. Step 5. Use the value of the test statistic and the rejection rule to determine whether to reject H0. One­Tailed Tests About a Population Mean: σ Known s Example: Metro EMS The response times for a random sample of 40 medical emergencies were tabulated. The sample mean is 13.25 minutes. The population standard deviation is believed to be 3.2 minutes. The EMS director wants to perform a hypothesis test, with a .05 level of significance, to determine whether the service goal of 12 minutes or less is being achieved. One­Tailed Tests About a Population Mean: σ Known p ­Value and Critical Value Approaches 1. Develop the hypotheses. 1. Develop the hypotheses. H0: µ < 1 2 Ha: µ > 1 2 2. Specify the level of significance. α = .05 3. Compute the value of the test statistic. x − µ 13.25 − 12 z= = = 2.47 σ / n 3.2 / 40 One­Tailed Tests About a Population Mean: σ Known p –Value Approach 4. Compute the p –value. For z = 2.47, cumulative probability = .9932. p–value = 1 − .9932 = .0068 5. Determine whether to reject H0. 5. Determine whether to reject Because p–value = .0068 < α = .05, we reject H0. There is sufficient statistical evidence to infer that Metro EMS is not meeting the response goal of 12 minutes. One­Tailed Tests About a Population Mean: σ Known • p –Value Approach Sampling distribution x − µ0 z of = σ/ n α = .05 p­value = .0 0 6 8 z 0 zα = 1.645 z = 2.47 One­Tailed Tests About a Population Mean: σ Known s Excel Formula Worksheet A Response 1 Time 2 19.5 3 15.2 4 11.0 5 12.8 6 12.4 7 20.3 8 9.6 9 10.9 10 16.2 11 13.4 12 19.7 B C Sample Size =COUNT(A2:A41) Sample Mean =AVERAGE(A2:A41) Population Std. Dev. 3.2 Hypothesized Value 12 Note: Rows 13­41 are not shown. Standard Error =C4/SQRT(C1) Test Statistic z =(C2-C5)/C7 p -Value (lower tail) =NORMSDIST(C8) p -Value (lower tail) =1-C10 p -Value (two tail) =2*(MIN(C10,C11)) One­Tailed Tests About a Population Mean: σ Known s Excel Value Worksheet A Response 1 Time 2 19.5 3 15.2 4 11.0 5 12.8 6 12.4 7 20.3 8 9.6 9 10.9 10 16.2 11 13.4 12 19.7 B C Sample Size 40 Sample Mean 13.25 Population Std. Dev. 3.2 Hypothesized Value 12 Standard Error 0.506 Test Statistic z 2.47 p -Value (lower tail) 0.9933 p -Value (upper tail) 0.0067 p -Value (two tail) 0.0134 Note: Rows 13­41 are not shown. One­Tailed Tests About a Population Mean: σ Known Critical Value Approach 4. Determine the critical value and rejection rule. For α = .05, z.05 = 1.645 Reject H0 if z > 1.645 5. Determine whether to reject H0. 5. Determine whether to reject Because 2.47 > 1.645, we reject H0. There is sufficient statistical evidence to infer that Metro EMS is not meeting the response goal of 12 minutes. p­Value Approach to Two­Tailed Hypothesis Testing Compute the p­value using the following three steps: 1. Compute...
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