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Optiontopic1 - BASIC BUSINESS STATISTICS BASIC BUSINESS...

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Unformatted text preview: BASIC BUSINESS STATISTICS BASIC BUSINESS STATISTICS Eleventh Edition Berenson Levine Krehbiel Slides Modified by Eugene Li Optional Topic 1 Optional Topic 1 Inferences About Population Variances s Hypothesis Test about the Variances of Two Populations (10.4) Slide 2 Hypothesis Testing About the Hypothesis Testing About the Variances of Two Populations s Hypotheses H 0 : σ 12 ≤ σ 22 H 0 : σ 12 = σ 22 H a : σ 12 > σ 22 s H a : σ 12 ≠ σ 22 Test Statistic Rejection Rule Reject H0 if: 2 s1 F= 2 s2 s F > Fα F > Fα/2 where the value of Fα and Fα/2 is based on an F distribution with n1 ­ 1 (numerator) and n2 ­ 1 (denominator) degrees of freedom. This rejection rule is for when we put the larger sample variance to the numerator Slide 3 Example: Buyer’s Digest Example: Buyer’s Digest Buyer’s Digest rates thermostats manufactured for home temperature control. In a recent test, 10 thermostats manufactured by ThermoRite and another 9 manufactured by TempKing were selected and placed in a test room that was maintained at a temperature of 68oF. The temperature readings of the twenty thermostats are listed below. We will conduct a hypothesis test with α = 0.05 to see if the variances are equal for ThermoRite’s thermostats and TempKing’s thermostats. ThermoRite: 67.4 67.8 68.2 69.3 69.5 67.0 68.1 68.6 67.9 67.2 TempKing: 66.4 67.8 68.2 70.3 69.5 68.0 68.1 68.6 67.9 Slide 4 Example: Buyer’s Digest s Hypothesis Testing About the Variances of Two Populations • Hypotheses 2 H 0 : σ 12 = (ThermoRite and TempKing thermo­ σ2 stats have same temperature variance) H a : σ 12 ≠ σ 22 (Their variances are not equal) • Test Statistic ThermoRite’s sample variance is .70 (d.f = 9). TempKing’s sample variance is 1.2111 (d.f. = 8). F = 1.2111/.70 = 1.7301 Slide 5 Example: Buyer’s Digest s Hypothesis Testing About the Variances of Two Populations • Rejection Rule The F distribution table shows that with α = .05, 8 d.f. (numerator), and 9 d.f. (denominator), F.025 =4.10. Reject H0 if F > 4.10 • Conclusion We fail to reject H0. We don’t have enough evidence to conclude that the population variances differ for the two thermostat brands. Slide 6 If not using the larger sample variance in the numerator, then…………. •The rejection region is F>Fα/ 2,ν 1,ν 2 or F<1/Fα/2 ,ν 2 ,ν 1 F > Fα / 2,ν 1,ν 2 = F.025,8,9 = 4.10 F< 1 Fα / 2,ν 2,ν 1 = 1 F.025,9,8 1 = = .2294 4.36 H a : σ 12 < σ 22 Note: F<1/Fα/2 ,ν 2 ,ν 1 is for testing , when we put the smaller sample variance on the numerator. Slide 7 The End of Optional Topic 1 The End of Optional Topic 1 Slide 8 ...
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