Question: In the General Social Survey people classified themselves as being very happy, pretty happy, or not too happy (variable happy). Consider the relationship between happiness and age.

a. Compare basic descriptive statistics for each of the three happiness groups.

b. Make boxplots of age for the three groups

c. Does the assumption of equal variances in the groups appear reasonable? The assumption of normality?

d. Perform a one-way analysis of variance on these data. What can you conclude? Which groups are significantly different from one another using the Bonferroni test?

e. From the analysis-of-variance table, estimate the variance of the ages within each happiness group. What is your estimate of the standard deviation within the groups? How does this compare to the actual standard deviations of each group in the table of descriptive statistics?

f. What are the three samples means that you have observed in the table of descriptive statistics? Based on the three sample means, what is your estimate of the variance of the ages within each happiness group?

g. What is the value of the ratio of the two variances?

h. If the null hypothesis is true, how often would you expect to see a ratio of sample variances at least this large?