The tortoise beetle Deloyala guttata feeds and lays eggs on leaves of the two morning glory species Ipomea pandurata and I. purpurea. Rausher (1984) investigated whether there was genetic variation in the population in the relative abilities of beetles to exploit the two plant species. To test this, he randomly sampled six beetle families from a local population by crossing randomly sampled males and females. He then raised half the offspring from each family on leaves of I. pandurata and the other half on I. purpurea. Here we analyze development time (the days from hatching to formation of the pupa) of female offspring from each family. If genetic variation is present in the relative abilities to exploit the two plant species, then there should be an interaction between family and plant species. Means are given in the table on page 635; standard errors were about 0.7.

a. Draw an interaction plot for these results. Briefly describe (in words) the patterns revealed. Is an interaction present? How can you tell?

b. Write a model statement for a “full” linear model to fit to these data. Explain what each term in the model represents.

c. Which factors in the linear model are random and which are fixed? Explain.

d. What are the null hypotheses to test in the corresponding ANOVA table?

e. What assumptions are required to test these hypotheses?

f. What does the F-statistic for any given term in the model signify?