Question

American Cranberry (Vaccinium macrocarpon) was used medicinally by Native Americans for the treatment of bladder and kidney ailments. A randomized controlled study was designed to test whether regular drinking of cranberry juice can prevent the recurrence of urinaty tract infections (UTIs) in women. A total of 145 women who were treated for antibiotics were enrolled in the study and randomly assigned to one of three treatment groups. One group drank cranberry juce concentrate daily for six month; another took a lactobacillus drink daily for six months (also potentially helpful in preventing recurrent UTIs); The last group (controls) drank neither cranberry juice concentrate or the lactobacillus drink.

	Outcome
Treatment	Recurring UTI	No New UTI
Cranberry Juice	8	42
Lactobacillus Drink	20	29
Control	20	26

Compute the exp frequencies for each cell in the table:

	Expected Counts
Treatment	Recurring UTI	No New UTI
Cranberry Juice	………..	…………..
Lactobacillus Drink	………….	………..
Control	…………….	………

Chi-Square = ……….. Use Table D to find the p-value of this statistic:

a)	p > .05. No evidence cranberry juice reduces the probability of recurrent UTIs.

b)	p < .05. Some evidence cranberry juice reduces the probability of recurrent UTIs.

c)	p < .01. Strong evidence cranberry juice reduces the probability of recurrent UTIs.

Answer 1

from above expected counts:

Ei=Σrow*Σcolumn/Σtotal	recurring	no new UTI
Cranberry	16.5517	33.4483
Lactobacillus	16.2207	32.7793
Control	15.2276	30.7724

applying chi square test:

chi square    χ2	=(Oi-Ei)2/Ei	recurring	no new UTI	Total
	Cranberry	4.4184	2.1864	6.605
	Lactobacillus	0.8806	0.4357	1.316
	Control	1.4957	0.7401	2.236
	Total	6.795	3.362	10.157

Chi-Square = 10.1569

option D p < .01. Strong evidence cranberry juice reduces the probability of recurrent UTIs.