The company sought to improve the quality of its production and claims that there are no more than $6\%$ defective light bulbs in its production. A consumer association conducts a test on a sample and obtains 71 defective light bulbs out of 1000.

\begin{enumerate}
  \item In the case where there would be exactly $6\%$ defective light bulbs, determine an asymptotic confidence interval at the $95\%$ level for the frequency of defective light bulbs in a random sample of size 1000.
  \item Do we have reasons to question the company's claim?
\end{enumerate}