In a particular region, 78 cases of SIDS (sudden infant death syndrome) were sampled. From the birth certificates, the mean birth weight in grams for these 78 cases was 2994 g. It is known that the standard deviation for all birth weights is 800 g. For the general population the average birth weight is 3300 g. We want to design a test of the null hypothesis that birth weight is 3300g against the alternative hypothesis that birth weight is 2994 g. What is the power of this two-sided test at the 5% level of significance? Is it appropriate? If not, what could you do to increase power?

**Subject Mathematics Applied Statistics**