In a given week, 12 babies are born in hospital. Assume that this sample came from an underlying normal population. The length of each baby is routinely measured and is listed below (in cm):

49, 50, 45, 51, 47, 49,48, 54, 53, 55, 45, 50

a. Find unbiased estimators for the mean and variance. The average length of babies is thought to be 50.5cm. There is a concern that this is an overestimate.

b. Test this claim at the 5% significance level based on this sample.