Suppose that a 100(1 − α) confidence interval for parameter θ is obtained as (L, R) with L = exp − Φ −1 (α/2) √ n X and R = exp Φ −1 (α/2) √ n X . (a) Using this, find a 100(1 − α) confidence interval for η = log θ. (b) What sample size is necessary in order that the interval that you found in (a) be no larger than length `?