# Chi-Square Practice Problems Or Extra Credit (19 Pts

Chi-square Practice Problems or Extra Credit (19 pts.)

Problem 1 - "Is There a Season for Homicide?"
Data File:Homicide-season

Criminologists have long debated whether there is a relationship between weather and violent crime. The author of the paper "Is There a Season for Homicide?" (Criminology (1988) : 287 - 296) classified 1361 homicides according to season, resulting in the following data. Does this data support the theory that the homicide rate is not the same over the four seasons? (4 pts.)

Winter / Spring / Summer / Fall / Total
328 / 334 / 372 / 327 / 1361

Problem 2 - Effects of Environment on the Claw Development in Lobsters
Data File: Lobster-claws.JMP

The two claws of the lobster (Homarus americanus) are identical in the juvenile stages. By adulthood, however, the two claws normally have differentiated into a stout claw called a "crusher" and slender claw called a "cutter". In a study of the differentiation process, 26 juvenile animals were reared in smooth plastic trays and 18 were reared in trays containing oyster chips (which they could use to exercise their claws.) Another 23 animals were reared in trays containing only one oyster chip. The claw configurations of all animals as adults are summarized in these data.

CLAW CONFIGURATION

TREATMENT / RCrush,LCut / RCut,LCrush / RCut,LCut / Row Totals
One oyster chip / 7 / 9 / 7 / 23
Oyster Chips / 8 / 9 / 1 / 18
Smooth Plastic / 2 / 4 / 20 / 26
Column Totals / 17 / 22 / 28 / n = 67

a) Contruct a mosaic plot for the relationship between treatment and claw configuration. Also calculate the conditional probabilities of the form P(claw configuation | treatment) and discuss the results. (2 pts.)

b) Perform a test to determine whether there is a relationship between the environment the lobster was reared in and the claw configuration when it reaches adulthood. Discuss your findings. (4 pts.)

Problem 3 – Comparison of Tooth Wear between Big Cats, Hyaenas, and Wolves/Wild Dogs

Excerpt from the paper “Incidence of Tooth Breakage Amongst Large, Predatory Animals” by Valkenburgh in the The American Naturalist is given below:

The sample is described as…

In this analysis you will be comparing wear stage across species, where wear stage is categorized as follows:

Question and Tasks for Problem 2 (Data File: Skull Tooth Wear)

a) Is there evidence to suggest that the species differ in terms of tooth wear? Use an appropriate test to answer this research question. Obtain the results using both the broad species and individual species categorization and then summarize your findings. (6 pts.)

b) Use correspondence analysis to construct a display showing the difference in tooth wear across individual species. Discuss what this plot, along with the mosaic plot, show regarding differences in wear between the species examined. (3 pts.)