Cranberry juice for preventing urinary tract infections. American cranberry (Vac
ID: 3229775 • Letter: C
Question
Cranberry juice for preventing urinary tract infections. American cranberry (Vaccinium macrocarpon) was used medicinally by Native Americans for the treatment of bladder and kidney aliments A randomized controlled study was designed to test whether regular drinking of cranberry juice can prevent the recurrence of urinary tract infections (UTIs) in women. One hundred and fifty women with a urinary tract inflection were treated with antibiotic and then randomly assigned to one of three groups One group drank cranberry juice concentrate daily far sot months; another group took a lactobacillus drink daily for six months (a lactose-fermenting bacterium thought to help Inhibit the growth of UTI-causing bacteria); the last group served as the control group and drank neither cranberry juice nor lactobacillus drinks for six months After six months, the number of women In each group with recurring symptomatic UTI (defined as one or more new infections) was recorded. Here are the results: Are the conditions for a chi-square goodness-of-fit test satisfied? Explanation ___________ What are the null and alternative hypotheses for this test? Null Hypothesis__________ Alternative Hypothesis_______ What are the expected counts under the null hypothesis? (Fill out Chart on the Right) What are the calculated Chi-Square Stats Observed vs. Expected Variances by Outcome? (Fill Out Chan on Right) What are the degrees of freedom for this test?__________ What is the Chi-Square Statistic for this Test?____________ Is there significant evidence that the treatment has an impact on the outcome of a UTI? Do you have any indication as to what forms your conclusion? Explanation ___________Explanation / Answer
a)
The chi-square goodness of fit test is appropriate when the following conditionsare met: The sampling method is simple random sampling. The variable under study is categorical. The expected value of the number of sample observations in each level of the variable is at least 5.
b)
H0: There is evidence that the treatment has not impact on the outcome of a UTI
H1: There is evidence that the treatment has impact on the outcome of a UTI
c) The expected frequencies are
e) degrees of freedom = (3-1)*(2-1) = 2
f) Chisquae contribution
Test Statistic, X^2: 7.2900
g)
P-Value: 0.0261 which is less than alpha 0.05,we reject Ho
Thus we conclude that there is evidence that the treatment has impact on the outcome of a UTI
Recurring No new Total Cranberry 15.101 34.899 50 Lactobacilus 14.799 34.201 49 Control 15.101 34.899 50 Total 45.001 103.999 149