At 8 weeks of age kittens at a specific shelter are assessed. A vet previously noted that the average weight of kittens (deemed healthy) at 8 weeks is 696.8 grams. A random sample of 9 kittens had an...

At 8 weeks of age kittens at a specific shelter are assessed. A vet previously noted that the average weight of kittens (deemed healthy) at 8 weeks is 696.8 grams. A random sample of 9 kittens had an average weight of 664.2 grams and a sample standard deviation of 71.5. She calls a colleague at an affiliated rescue in another county to see if anything is happening with their kittens at 8 weeks of age. They observe that from a sample of 22 healthy independent kittens an average weight of 735.1g with a sample standard deviation of 82.5g. Assume the distribution of kitten weights at 8 weeks is sufficiently close to the normal distribution to use the CLT, and that kittens are independent (statistically, not literally)

Question:
Suppose we anticipate equal number of kitten in shelter A and shelter B. The true difference in the average weights of kittens is 10.0g, and the true standard deviation were 100.0g and 120.0g, respectively. Calculate the total sample size required in both shelters if a two-sided test is used with a 5% signicance level and an 80% power is desired