A study is being performed to assess the effectiveness of a new medication to relieve pain from arthritis. Researchers recruit 300 subjects suffering from arthritis. They randomly assign half of the subjects to receive the new medication, and half to receive a placebo. After one hour, they record whether or not each patient is experiencing pain relief. The results are given in the table below. Pain relief No pain relief New medication 51 99 Placebo 28 122 a) Calculate a 99% confidence interval for percentage of subjects in each population who have pain relief after one hour (keeping the two groups separate). State each confidence interval in a sentence. b) Do the confidence intervals overlap? How can you interpret the results of this study, based on whether there is or is not any overlap? c) Suppose the researchers conducted appropriate hypothesis testing (covered later in this course), and found that there was a statistically significant difference in the percentage of subjects experiencing pain relief between subjects receiving the new medication and subjects receiving the placebo. Could they conclude that this difference was caused by the new medication? Briefly explain your answer.