Answer
a) The claim is supported.
b) The claim is supported.
c) The treatment is effective.
Work Step by Step
a) We want to see if the mean is different to $\frac{29}{148}=0.1959$, so we know $H_0:μ=0.1959$ and $H1:μ\gt0.1959$. We now use a Ti-84 calculator. To solve, go to "Stat," then "Tests," and then select "Stats." Doing this, we can find that the critical value and use a z-table calculator to find that $p=0.0000\lt0.05$, hence the claim is valid.
b) We use a ti-84 calculator to find the confidence interval. To do this, we press “Stat” and then select “Tests.” Next, we select “2-PropZInt” to conduct the test. Doing this, we can find that the $0.467\lt \mu\lt0.687$. This is bigger than $0$, meaning that the treatment does improve the patient's well-being.
c) The results show that the treatment works and does, indeed, help treat headaches.
