An experimenter wishes to obtain a confidence interval for the difference between true average breaking strength for cables manufactured by company A and company B. Suppose breaking strength is normally distributed for both types of cable with sigma_A 30 psi and sigma_B = 20 psi.

a. If costs dictate that sample size for type A cable should be three times the sample size for the type B cable, how many observations are required if the length of 99% confidence interval is to be at most 20 psi?
b. Suppose 400 observations are to be made. How many of the observations should be made on type A cable samples if the length of the resulting 99% confidence interval is to be minimum?