Cranberry juice. It's common folk wisdom that drinking cranberry juice can help prevent urinary tract infections in women. In 2001 the British Medical Journal reported the results of a Finnish study in which three groups of 50 women were monitored for these infections over 6 months. One group drank cranberry juice daily, another group drank a lactobacillus drink, and the third drank neither of those beverages, serving as a control group. In the control group, 18 women developed at least one infection, compared to 20 of those who consumed the lactobacillus drink and only 8 of those who drank cranberry juice. Does this study provide supporting evidence for the value of cranberry juice in warding off urinary tract infections?

a) Is this a survey, a retrospective study, a prospective study, or an experiment? Explain.

b) Will you test goodness-of-fit, homogeneity, or independence?

c) State the hypotheses.

d) Check the conditions.

e) How many degrees of freedom are there?

f) Find and the P-value.

g) State your conclusion.

h) If you concluded that the groups are not the same, analyze the differences using the standardized residuals of your calculations.