Denote x and y asthepopulationvariancesinthetwosample

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Unformatted text preview: m the F‐distribution that satisfies: 16 P( F( n x − 1 , n y − 1 ) > Fc ) = α Chapter 11 Example: Exercise 11.28, page 393 of the textbook Annual total sales of a company are reported for two sample periods: Period 1: active price competition in the industry (4 years) Period 2: price collusion in the industry (7 years) It is hypothesized that total sales should vary more in an industry with active price competition compared to a market with price collusion. Denote σ X and σ Y as the population variances in the two sample 2 2 periods. Test the null hypothesis: H0 : σ 2 = σ 2 against the alternative: H1 : σ 2 > σ 2 X Y X Y From the data set, the sample statistics are: Period 1: n x = 4 s2 = 114.09 x s x = 10.68 Period 2: n y = 7 s2 = 16.08 y s y = 4.01 17 Chapter 11 The test statistic is the variance ratio: s2 114.09 x = 7.095 2= s y 16.08 This can be compared with the critical values reported in Appendix Table 9 for the F‐distribution. For a 5% significance level, wit...
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