# A.3.2.3 Analyzing a Study With Two Treatments

In an experiment to test the effectiveness of vitamin C on the length of colds, two groups of people with colds are given a pill to take once a day. The pill for one of the groups contains 1,000 mg of vitamin C, while the other group takes a placebo pill. The researchers record the results in a table. (A placebo pill is a pill that looks just like the one that has the vitamin C, but does not actually have any vitamin C in it) In this study, the person taking it does not know which pill is which.

First, the researchers want to know what percentage (to the nearest whole percent) of people are in each combination of categories. Fourteen percent of all the participants had a cold that lasted less than a week and were in group A. What percentage of all the participants had a cold that lasted less than a week and were in group B? Complete the rest of the relative frequency table with the corresponding percentages.

Next, the researchers notice that, among participants who had colds that lasted less than a week, 37% were in group A. Among participants who had colds that lasted a week or more, what percentage were in group B? Complete the table with the corresponding percentages.

Finally, the researchers notice that, among the participants in group A, 48% had colds that lasted less than one week. Among the participants in group B, how many had colds that lasted a week or more? Complete the table with the corresponding percentages.

To understand the results, the researchers want to know: Among people whose colds lasted less than a week, what percentage are in group B? Explain your reasoning.

If the researchers believe that vitamin C has a small effect on the length of a cold, which group most likely got the pills containing vitamin C? Explain your reasoning.