In a study of users’ adoption of a new app feature, researchers claim that the true adoption rate $p$ is greater than $30\%$. They collect a sample of $n=100$ users and find a sample proportion $\hat{p}=0.35$. At $\alpha =0.05$, can they use the normal approximation, and do the data support the claim?

The normal approximation can be used, but the data do not support the claim that the adoption rate exceeds $30\%$ at $\alpha =0.05$.

The normal approximation cannot be used, and the data support the claim that the adoption rate exceeds $30\%$ at $\alpha =0.05$.

The normal approximation can be used, and the data support the claim that the adoption rate exceeds $30\%$ at $\alpha =0.05$.

The normal approximation cannot be used, and the data do not support the claim that the adoption rate exceeds $30\%$ at $\alpha =0.05$.