Question

The following output summarizes the results for a one-way analysis of variance experiment in which the treatments were three different hybrid cars and the variable measured was the miles per gallon (mpg) obtained while driving the same route. (You may find it useful to reference the q table.)

Hybrid 1: x¯1x¯1 = 25, n₁ = 20
Hybrid 2: x¯2x¯2 = 35, n₂ = 15
Hybrid 3: x¯3x¯3 = 21, n₃ = 18

The following output summarizes the results for a one-way analysis of variance experiment in which the treatments were three different hybrid cars and the variable measured was the miles per gallon (mpg) obtained while driving the same route. (You may find it useful to reference the gtable.) Hybrid 1: 2 1 = 25, n1-20 Hybrid 2: - 35, n2 15 Hybrid 3: -21, n3 18 Source of Variation Between Groups Within Groups Total df 2 50 52 MS 570.38 26.70 p-value 0.0000 1,140.76 1,335.03 2,475.79 21.36 a. At the 1% significance level, can we conclude that average mpg differs between the hybrids? OYes since the p-value is less than the significance level OYes since the p-value is not less than the significance level. O No , since the p-value is less than the significance level O No , since the p-value is not less than the significance level. b. Use Tukey's HSD method at the 1% significance level to determine confidence intervals for the population mean differences and state which individual pairs of hybrids' means differ. (If the exact value for nT c is not found in the table, then round down Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.) Population Mean Differences Can we conclude that the hybrids' means differ? Confidence Interval H1 H3 H2 -H3

Answer 1

a)

yes since the p value is less than singificance level

b)

			Lower bound	Upper bound	differ
			|xi-xj|-LSD	|xi-xj|-LSD
μ1-μ2			-15.39	-4.61	significant difference
μ1-μ3			-1.12	9.12	not significant difference
μ2-μ3			8.49	19.51	significant difference