Answer
a) The claim is not supported.
b) The claim is not supported.
c) No, it is not.
Work Step by Step
a) We want to see if the mean is different to $\frac{277}{1524}=0.1818$, so we know $H_0:μ=0.1818$ and $H1:μ\lt0.1818$. 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 $p\gt0.01$, so the claim is not supported.
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 confidence interval goes through $0$, so the claim is not supported.
c) The results show that it does not have an impact on preventing dementia.
