Do people who go to bars and pubs a lot tend to have more friends? A recent GSS asked, €œHow often do you go to a bar or tavern?€ The table shows results of ANOVA for comparing the mean number of good friends at three levels of this variable. The very often group reported going to a bar at least several times a week. The occasional group reported going occasionally, but not as often as several times a week.
Summary of ANOVA for mean number of good friends and going to bars

a. State the
(i) Hypotheses,
(ii) Test statistic value, and
(iii) P-value for the significance test displayed in this table. Interpret the P-value.
b. Based on the assumptions needed to use the method in part a, is there any aspect of the data summarized here that suggests that the ANOVA test and follow-up confidence intervals may not be appropriate? Explain.

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Mean Standard dev. Sample size Very often 12.1 21.3 Occasional 6.4 10.2 166 Never 6.2 14.0 215 41 Source Group Error Total DE MS 0.049 2 1116.8 558.4 3.03 419 77171.8 184.2 421 78288.5