Chapter+9

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Unformatted text preview: ple: Highway Patrol s One­Tailed Test About a Population Mean: σ Unknown At Location F, a sample of 64 vehicles shows a mean speed of 66.2 mph with a standard deviation of 4.2 mph. Use α = .05 to test the hypothesis. One­Tailed Test About a Population Mean: One­Tailed Test About a Population Mean: σ Unknown p –Value and Critical Value Approaches 1. Determine the hypotheses. H0: µ < 65 Ha: µ > 65 2. Specify the level of significance. α = .05 3. Compute the value of the test statistic. t= x − µ0 66.2 − 65 = = 2.286 s / n 4.2 / 64 One­Tailed Test About a Population Mean: One­Tailed Test About a Population Mean: σ Unknown p –Value Approach 4. Compute the p –value. For t = 2.286, the p–value must be less than .025 (for t = 1.998) and greater than .01 (for t = 2.387). .01 < p–value < .025 5. Determine whether to reject H0. Because p–value < α = .05, we reject H0. We are at least 95% confident that the mean speed of vehicles at Location F is greater than 65 mph. One­Tailed Test About a Population Mean: σ Unknown s 1 2 3 4 5 6 7 8 9 10 11 12 13 Excel Formula Worksheet A B Speed Sample Size 69.6 Sample Mean 73.5 Sample Std. Dev. 74.1 64.4 Hypoth. Value 66.3 68.7 Standard Error 69.0 Test Statistic t 65.2 Degr. of Freedom 71.1 70.8 p -Value (lower tail) 64.6 p -Value (upper tail) 67.4 p -Value (two tail) C =COUNT(A2:A65) =AVERAGE(A2:A65) =STDEV(A2:A65) 65 =C3/SQRT(C1) =(C2-C5)/C7 =C1-1 =IF(C8<0,TDIST(-C8,C9,1),1-TDIST(C8,C9,1)) =1-C11 =2*MIN(C11,C12) Note: Rows 14­65 are not shown. One­Tailed Test About a Population Mean: σ Unknown s 1 2 3 4 5 6 7 8 9 10 11 12 13 Excel Value Worksheet A B Speed Sample Size 69.6 Sample Mean 73.5 Sample Std. Dev. 74.1 64.4 Hypoth. Value 66.3 68.7 Standard Error 69.0 Test Statistic t 65.2 Degr. of Freedom 71.1 70.8 p -Value (lower tail) 64.6 p -Value (upper tail) 67.4 p -Value (two tail) C 64 66.2 4.2 65 0.525 2.286 63 0.9872 0.0128 0.0256 Note: Rows 14­65 are not shown. One­Tailed Test About a Population Mean: σ Unknown Critical Value Approach 4. Determine the critical value and rejection rule. For α = .05 and d.f. = 64 – 1 = 63, t.05 = 1.669 Reject H0 if t > 1.669 5. Determine whether to reject H0. Because 2.286 > 1.669, we reject H0. We are at least 95% confident that the mean speed of vehicles at Location F is greater than 65 mph. Location F is a good candidate for a radar trap. One­Tailed Test About a Population Mean: σ Unknown Reject H0 Do Not Reject H0 0 α = .0 5 tα = 1.669 t A Summary of Forms for Null and Alternative Hypotheses About a Population Proportion s The equality part of the hypotheses always appears in the null hypothesis. In general, a hypothesis test about the value of a population proportion p must take one of the following three forms (where p0 is the hypothesized value of the population proportion). H 0 : p ≥ p0 H a : p < p0 H 0 : p ≤ p0 H a : p > p0 H 0 : p = p0 H a : p ≠ p0 One­tailed (lower tail) One­tailed (upper tail) Two­tailed Tests Ab...
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This note was uploaded on 08/28/2011 for the course BUS 300 taught by Professor White during the Spring '09 term at Rutgers.

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