A researcher is studying the variability in blood glucose levels between two groups of diabetic patients. Group A ($n=51$) receives a new medication, while group B ($n=51$) receives a placebo. The standard deviation of blood glucose levels in group A is $22.5\text{ mg/dL}$, and in group B it is $15.3\text{ mg/dL}$. Assume blood glucose levels are normally distributed. At the $\alpha =0.01$ significance level, is the standard deviation in group A significantly higher than in group B?