Question

1. To determine the reasons for the apparent disappearance of certain species of flies in winter in some temperate regions, Izquierdo (1991) conducted a study of the survival pattern of D. melanogaster in temperate regions under unfavorable winter conditions. Samples of male and female flies were selected from three population cages: one kept at 24^o C (cage I), one at 17^o C (cage II), and one at the site of fly collection (cage III). Flies selected from each cage were placed in bottles, and the bottles were kept at 4^o C under natural light conditions. Each bottle contained 50 flies. The number of survivors at the end of 45 days is shown in the table below and given in data flies.dta.

	Gender
	Male	Female
I (24oC)	26	22
	22	11
	27	8
	24	14
	27	14
II (17oC)	25	11
	35	16
	27	14
	32	16
	32	18
III (environmental)	33	6
	32	14
	33	12
	25	5
	28	16

1. Identify the factors and their levels in this study.
2. Plot the mean responses in a graph in which the cages are marked on the horizontal axis. Connect the three mean responses (at three cage temperature) for each gender with a straight line. Examine the graph to see if the difference between the mean survival numbers of males and females varies with the type of cage.
3. Suggest two hypotheses that can be verified using a factorial analysis of these data.
4. Perform all appropriate hypothesis tests using ANOVA. Show the ANOVA table, and draw your conclusions.

Compare the mean survival numbers in environmental conditions with the survival numbers at 24^o and 17^o (Be sure to take into consideration of the presence or absence of interaction between gender and type of cage. Do not adjust for multiple comparisons here). Obtain the 95% CI for these contrasts.

Answer 1

a) There are 3 factors under study each at 2 levels.

c) Null Hypothesis: H0A- There is no significant difference between the mean survival rate of males.

H1A- There is a significant difference between the mean survival rate of males.

H0B- There is a significant difference between the mean survival rate of females.

H1B- There is a s significant difference between the female survival rate.

H0C- There is no significant difference between the male and female survival rate.

H1C- There’s a significant difference between the male and female survival rate.