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 urinary tract infections (UTIs) in women. In the study, 150 women with a urinary tract infection were treated with antibiotic and then randomly assigned to one of three groups. One group drank cranberry juice concentrate daily for six months; another group took a Lactobacillus drink daily for six months (Lactobacillus is 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 Outcome
Treatment Recurring UTI No new UTI Total
Cranberry juice 8 42 50
Lactobacillus drink 19 30 49
Control 18 32 50
To access the complete data set, click the link for your preferred software format:
Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt!
(a) Find the percent of women not experiencing any new UTIs in each of the three treatment groups. (Enter your answers rounded to one decimal place.)
Cranberry juice treatment: %
Lactobacillus drink treatment: %
Control:
(b) What does the null hypothesis for the chi‑square test say about treatment outcome?
a. The null hypothesis says that there are equal numbers of women in the three treatment groups, that do not experience any new UTIs.
b. The null hypothesis says that equal proportions of women drinking the cranberry juice daily experience recurring UTI or no new UTI.
c. The null hypothesis says that equal proportions of women in the three treatment groups do not experience any new UTIs.
d. The null hypothesis says that equal proportions of women in the no new UTI and recurring UTI groups were treated with the three different treatments.
2. Individuals who have experienced a stroke are at an increased risk of having another stroke. Prevention is particularly important for high‑risk populations. The Second European Stroke Prevention Study asked whether daily doses of an anti‑blood‑clotting agent, such as aspirin or dipyridamole, would help prevent strokes among patients who had just experienced a first stroke. Volunteer patients were randomly assigned to one of four treatment options, including a placebo. Researchers recorded how many patients experienced another stroke and how many died of a stroke during the two years of the study.
The Minitab output gives the observed and expected counts for this study, along with the chi‑square calculations.
Stroke NoStroke Total Death NoDeath Total
Placebo 250 1399 1649 Placebo 202 1447 1649
205.81 1443.19 189.08 1459.92
Aspirin 206 1443 1649 Aspirin 182 1467 1649
205.81 1443.19 189.08 1459.92
Dipyr. 211 1443 1654 Dipyr. 188 1466 1654
206.44 1447.56 189.65 1464.35
Both 157 1493 1650 Both 185 1465 1650
205.94 1444.06 189.19 1460.81
Total 824 5778 6602 Total 757 5845 6602
ChiSq = 9.487 + 1.353 + ChiSq = 0.883 + 0.114 +
0.000 + 0.000 + 0.265 + 0.034 +
0.101 + 0.014 + 0.014 + 0.002 +
11.629 + 1.658 + = 24.243 0.093 + 0.012 = 1.418
df = 3, p = 0.000 df = 3, p = 0.701
SOLVE: Do the expected counts under the null hypothesis satisfy the conditions for using a chi‑square test?a. Yes. All expected counts are less than 55 , so the chi‑square test is appropriate. b. No. All expected counts are greater than 55 , so the chi‑square test is not appropriate. c. No. All expected counts are less than 55 , so the chi‑square test is not appropriate. d. Yes. All expected counts are greater than 55 , so the chi‑square test is appropriate. Use the given software output to determine if the 2χ2 test is statistically significant. Select the correct answer. a. P<0.001P<0.001 indicates that the 2χ2 test is not statistically significant. b. P<0.701P<0.701 indicates that the 2χ2 test is statistically significant. c. P=0.701P=0.701 indicates that the 2χ2 test is statistically significant. d. P<0.001P<0.001 indicates that the 2χ2 test is statistically significant. CONCLUDE: Which choice is an appropriate summary of your overall findings?a. There is significant evidence that the combination of aspirin and dipyridamole is effective at decreasing the risk of stroke. There is not enough evidence that each of these two anti‑blood‑clotting agents is effective when given alone. b. The study proves that the combination of aspirin and dipyridamole is most effective at decreasing the risk of stroke. c. Treatment choice significantly impacts stroke outcome. The combination of aspirin and dipyridamole was shown to be effective at decreasing the risk of stroke. d. There is no statistical evidence of a difference in proportions of stroke among individuals given the four treatments.