1)Researchers want to test the effectiveness of a new anti-anxiety medication. Four hundred twenty patients were recruited to participate in the clinical trial. In clinical testing, 70 out of 220 people taking the medication reported symptoms of anxiety. Of the other 200 people receiving a placebo, 105 reported symptoms of anxiety. Combining the two samples together, what is the overall proportion of those who reported symptoms of anxiety among all participants?

2)Researchers want to test the effectiveness of a new anti-anxiety medication. Four hundred twenty patients were recruited to participate in the clinical trial. In clinical testing, 70 out of 220 people taking the medication reported symptoms of anxiety. Of the other 200 people receiving a placebo, 105 reported symptoms of anxiety. What is the estimated standard error of the difference of the two sample proportions based onpooled sample proportion?

3)Researchers want to test the effectiveness of a new anti-anxiety medication. Three hundred eighty patients were recruited to participate in the clinical trial and were randomly assigned to two groups, of which one received the medication, and the other, a placebo. In clinical testing, 53 out of 200 people taking the medication reported symptoms of anxiety. Of the other 180 people receiving a placebo, 86 reported symptoms of anxiety. If we use P1 to denote the population proportion of those who receive the medication and P2 of those who receive placebo, what would be your 95% Confidence Interval estimate for P1-P2 based on the given information? Please note that to estimate the standard error of the difference of the sample proportions you will use the two individual sample proportions instead of the pooled sample proportion. (Hint: Use 1.96 as your critical z-value)

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