Experimental studies of cancer often use strains of animals that have a naturally high incidence of tumors. In one such experiment, tumor-prone mice were kept in a sterile environment; one group of mice was maintained entirely germ free, while another group was exposed to the intestinal bacterium Escherichia coli. The accompanying table shows the incidence of liver tumors.

(a) How strong is the evidence that tumor incidence is higher in mice exposed to E. coli? Use a chi-square test against a directional alternative following the five steps (a-e) in Exercise 10.2.4. Let α = 0.05.
(b) How would the result of part (a) change if the percentages (39% and 62%) of mice with tumors were the same, but the sample sizes were
(i) Doubled (98 and 26)?
(ii) Tripled (147 and 39)?

Transcribed Image Text:

Mice with liver tumors Number Treatment Germ free E, coli Total number of mice 49 13 Percent 39% 62% 19