Step 1

Medication:

Reduction \(\displaystyle={30},\text{no reduction}={20},\text{total}={50}\)

Placebo:

Reduction \(\displaystyle={15},\text{no reduction}={35},\text{total}={50}\)

RR: Relative Risk \(\displaystyle=\frac{{\frac{30}{{50}}}}{{\frac{15}{{50}}}}={2}\) (Assuming the reduction of of symptoms as incidence in each of the medication and placebo groups)

Step 2

The \(95\%\) confidence interval for ln(RR) is given by :

ln \(\displaystyle{\left({2}\right)}\pm{1.96}{\left(\sqrt{{{\left[{\left(\frac{{\frac{20}{{30}}}}{{50}}\right)}+{\left(\frac{{\frac{35}{{15}}}}{{50}}\right)}\right]}}}\right)}\)

\(\displaystyle= \ln{{\left({2}\right)}}\pm{0.48}\)

\(\displaystyle={0.693}\pm{0.480}\)

\(\displaystyle={\left({0.693}-{0.480},{0.693}+{0.480}\right)}\)

\(\displaystyle={\left({0.213},{1.173}\right)}\)

Thus, the confidence interval for RR is antilog of the above values \(\displaystyle={\left({1.237},{3.232}\right)}\)

Hence the statement mentioned is false as the values don't match

Medication:

Reduction \(\displaystyle={30},\text{no reduction}={20},\text{total}={50}\)

Placebo:

Reduction \(\displaystyle={15},\text{no reduction}={35},\text{total}={50}\)

RR: Relative Risk \(\displaystyle=\frac{{\frac{30}{{50}}}}{{\frac{15}{{50}}}}={2}\) (Assuming the reduction of of symptoms as incidence in each of the medication and placebo groups)

Step 2

The \(95\%\) confidence interval for ln(RR) is given by :

ln \(\displaystyle{\left({2}\right)}\pm{1.96}{\left(\sqrt{{{\left[{\left(\frac{{\frac{20}{{30}}}}{{50}}\right)}+{\left(\frac{{\frac{35}{{15}}}}{{50}}\right)}\right]}}}\right)}\)

\(\displaystyle= \ln{{\left({2}\right)}}\pm{0.48}\)

\(\displaystyle={0.693}\pm{0.480}\)

\(\displaystyle={\left({0.693}-{0.480},{0.693}+{0.480}\right)}\)

\(\displaystyle={\left({0.213},{1.173}\right)}\)

Thus, the confidence interval for RR is antilog of the above values \(\displaystyle={\left({1.237},{3.232}\right)}\)

Hence the statement mentioned is false as the values don't match