= 4. The average birth weight of a newborn baby in the USA is reported to be 7.5 lbs. A random sample of n 200 newborn babies was taken in a southern state. It is found that their average birth weight was 7.32 lbs with a standard deviation 2.16 lbs. Let μl denote the average birth weight in this state. Perform a statistical test at a a = 0.05 level of significance to see if the average birth weight in this state matches well with the national average. (a) State the null and alternative hypotheses. (b) Let Z = X - μο s/√n be the z-test statistic. What is the null distribution of Z under Ho? What is the distri- bution of Z if μ = 7.2 in fact? (c) Compute the observed Z test statistic. Specify the rejection rule and draw conclusion accordingly. (d) Obtain the corresponding p-value.