Question

Substances to be tested for cancer-causing potential are often painted on the skin of mice. The question arose whether mice might get an additional dose of the substance by licking or biting their cagemates. To answer this question, the compound benzo(a)pyrene was applied to the backs of 10 mice: 5 were individually housed, and 5 were group-housed in a single cage. After 48 hours, the concentration of the compound in the stomach tissue of each mouse was determined. The results (nmol/gm) were as follows:

Singly housed	Group housed
3.3	3.9
2.4	4.1
2.5	4.8
3.3	3.9
2.4	3.4

Carry out the calculations required to compare the two groups using a Wilcoxon rank sum test. State the null and alternative hypotheses for the appropriate one-sided test. Calculate the test statistic. Using the function pwilcox() in R, calculate the p-value corresponding to this statistic. Assuming the desired Type I error level is 0.05, do these data provide enough evidence to reject the null hypothesis?

Answer 1

Substances to be tested for a cancer-causing potential are often painted on the skin of mice. The question arose whether mice might get an additional dose of the substance by licking or biting their cagemates. To answer the question, the compound benzoapyrene was applied to the backs of 10 mice: five were individually housed and 5 were group-housed in a single cage. After 48 hours, the concentration of the compound in the stomach tissue of each mouse was determinedH0: There is no diffeence between two means

H1:There is a difference betwween two means

Alpha:5%

Test statistic:

From Excel

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Single	5	13.9	2.78	0.227
Group	5	20.1	4.02	0.257
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	3.844	1	3.844	15.8843	0.004031	5.317655
Within Groups	1.936	8	0.242
Total	5.78	9

F cal=15.88

Conclusion:

P value=0.004

p<alpha we reject the null hypothesis., The claim is significant