STATISTICAL METHODS FOR BUSINESS UNIT 10 .- PARAMETRIC TESTS. 10.1 .- Tests for the mean. 10.2 .- Tests for the proportion. 10.3 .- Tests for the variance. Universidad de Oviedo. Facultad de Economía y Empresa. Grado en ADE. Métodos Estadísticos para la Empresa UNIT 10. GOALS • Solve statistical testing problems for the mean, proportion and variance. Universidad de Oviedo. Facultad de Economía y Empresa. Grado en ADE. Métodos Estadísticos para la Empresa One-tailed test for the mean H0 : µ ≥ µ0 H1 : µ < µ0 •P-VALUE APPROACH d • Obtain the test statistic * X • Obtain the p-value ( p = P dX < d /H0 * X ) If the p-value is small, then the null hypothesis is rejected Universidad de Oviedo. Facultad de Economía y Empresa. Grado en ADE. Métodos Estadísticos para la Empresa Two-tailed test for the mean H0 : µ = µ0 H1 : µ ≠ µ0 •P-VALUE APPROACH • Obtain the test statistic d * X •Obtain the p-value ( p = P dX > d /H0 * X ) N(0,1) tn-1 u Normal population, σ is known u Unknown distribution but σ is known and n is large u Normal population, σ is unknown If the p-value is small, then the null hypothesis is rejected Universidad de Oviedo. Facultad de Economía y Empresa. Grado en ADE. Métodos Estadísticos para la Empresa Two-tailed test for the proportion H0 : p = p 0 H1 : p ≠ p 0 •P-VALUE APPROACH • Obtain the test statistic d* dpˆ = pˆ − p p(1− p) n ≈ N(0,1) d pˆ pˆ - p0 p̂ = ≈ N(0,1) H0 p0 (1- p0 ) n •n is large •Obtain the p-value ( p = P dpˆ > dp*ˆ /H0 ) If the p-value is small, then the null hypothesis is rejected Universidad de Oviedo. Facultad de Economía y Empresa. Grado en ADE. Métodos Estadísticos para la Empresa Two-tailed test for the variance H0 : σ ≥ σ 2 H1 : σ < σ 2 0 2 2 0 •P-VALUE APPROACH • Obtain the test statistic dS* 2 •Obtain the p-value ( p = P dS < d /H0 χ 2 n− −1 2 * S2 ) u Normal population If the p-value is small, then the null hypothesis is rejected Universidad de Oviedo. Facultad de Economía y Empresa. Grado en ADE. Métodos Estadísticos para la Empresa Two-tailed test for the variance H0 : σ = σ H1 : σ ≠ σ 2 2 0 2 2 0 •P-VALUE APPROACH • Obtain the test statistic d* •Obtain the p-value dS* 2 •• ( d p = 2 P dS2 < d /H0 * S2 ) ( * S2 •• p = 2 P dS2 > dS* 2 /H0 ) If the p-value is small, then the null hypothesis is rejected Universidad de Oviedo. Facultad de Economía y Empresa. Grado en ADE. Métodos Estadísticos para la Empresa