A study about smoking and personality used a sample of 1638 adults in the Baltimore Longitudinal Study on Aging. The subjects formed three groups according to smoking status (never, former, current). Each subject completed a personality questionnaire that provided scores on various personality scales designed to have overall means of about 50 and standard deviations of about 10. The table shows some results for three traits, giving the means with standard deviations in parentheses.

a. For the F test for the extraversion scale, using the 0.05 significance level, what conclusion would you make?
b. Refer to part a. Does this mean that the population means are necessarily equal?

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Never Former smokers smokers smokers (11 828) (11:#694) (11 116) 46.7 (9.6 48.5 9.2) 51.9 (9.9) Current Neuroticism Extraversion 50.4 (10.3) 50.2 (10.0) 50.9 (9.4) 0.24 Conscientiousness 51.8 (10.1) 48.9 (9.7) 45.6 (10.3) 29.42 17.77