The masses, in kilograms, of newborn babies in country A are represented by the random variable \(X\), with mean \(\mu\) and variance \(\sigma^2\). The masses of a random sample of 500 newborn babies in this country were found and the results are summarised below. \[n=500,\qquad\sum x=1625,\qquad\sum x^2=5663.5.\]

(a) Calculate unbiased estimates of \(\mu\) and \(\sigma^2\). [3]

A researcher wishes to test whether the mean mass of newborn babies in a neighbouring country, B, is different from that in country A. He chooses a random sample of 60 newborn babies in country B and finds that their sample mean mass is 2.95 kg.

Assume that your unbiased estimates in part (a) are the correct values for \(\mu\) and \(\sigma^2\). Assume also that the variance of the masses of newborn babies in country B is the same as in country A.

(b) Carry out the test at the 1% significance level. [5]