Answer
a) The claim cannot be supported.
b) The claim cannot be supported.
c) No
Work Step by Step
a) We want to see if the mean is different to $\frac{40}{45}=0.8889$, so we know $H_0:μ=0.8889$ and $H1:μ\ne0.8889$. 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 $p=0.5720$. $p\gt0.05$, hence 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 is $−0.0798\lt μ_1−μ_2\lt0.149$. This goes through $0$, so we can see that there is not a significant difference.
c) The results show that it does not have an impact on infection rate.