1 . Two baby -food manufacturers are competing , and manu facturer of b rand A believes that their brand causes more weight gain in infants than manufacturer of brand B . A sample of size 15 fed their babies brand A for two months and saw an average weight gain of 36.93 ounces , with a standard deviation of 4 . 23 ounces . A sample of size 25 fed their babies brand B and saw an average weight gain of 31 36 ounces with a standard deviation of 3 .35 ounces Assume the standard deviations reported are true popu lation values ( a ) Create a 95% confidence interval for the difference in weight gain between the two baby food brands ( b ) Interpret your interval from ( a ) in terms of the prob - Tem ( C ) Do we know the probability that the true difference in averages lies within the interval calculate in ( a ) ? Explain ( d ) What assumptions did we need to make for this con fidence interval , and why