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 than $\frac{277}{1524}=.1818$, so we know $H_0: \mu = .1818$ and $H_1: \mu \lt .1818$. We now use a Ti-84 calculator. To solve, go to "Stat," then "Tests," and then select "Stats." Doing this, we find that the critical value and use a z-table calculator to find that p is more than .01, so the claim is not supported.
b. We use a ti-84 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 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.