A New Apparatus Has Been Devised to Replace the Needle $.07$

Essay

A new apparatus has been devised to replace the needle in administering vaccines. The apparatus, which is connected to a large supply of vaccine, can be set to inject different amounts of the serum, but the variance in the amount of serum injected to a given person must not be greater than $.07$ to ensure proper inoculation. A random sample of 25 injections was measured. Suppose the $p$ -value for the test is $p = .0031$ . State the proper conclusion using $\alpha = .01$ .