3 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.
$$n = 500 \quad \Sigma x = 1625 \quad \Sigma x ^ { 2 } = 5663.5$$
- Calculate unbiased estimates of \(\mu\) and \(\sigma ^ { 2 }\).
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 \(A\). - Carry out the test at the \(1 \%\) significance level.