1 Test the claim that the mean gas MPG (city) is equal for all three car sizes.

Question

1 Test the claim that the mean gas MPG (city) is equal for all three car sizes. This requires the use of one-way ANOVA (single factor) 2 to test for equality of three or more means (12.2) Small Midsize Large ANOVA Output Anova: Single Factor 19 20 21 21 25 18 25 25 29 SUMMARY 15 17 16 16 Small Midsize Large 173 24.7143 8.90476 142 20.2857 2.2381 19 19 20 ANOVA F aF 209.81 Within Gr 78.8571 2 104.905 23.9457 8.SE-06 3.55456 e frequencies are eq 18 4.38095 Total 288.667 es are not Test Statistic | #VALUE! Critical Value1.72074 P-Value Conclusion

Explanation / Answer

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Test statistic : F-value = MSbetween/MSwithin = 104.905/4.38095 = 23.9457

I will use Excel formula to solve the problem.

p-value = p(F,df1,df2) = p(23.9457,2,18) = 1-F.DIST(23.9457,2,18,TRUE) = 8.47*10^-6

The critical value is got by this formula: = F.INV(0.95,2,18) = 3.5546

Conclusion: The p-value if less than .05 means that the ANOVA is significant.

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