3. A park ranger wants to know the average size of trout in a certain lake. How large a sample of trout must be taken with 94% confidence so the sample mean will not be off by
more than 0.4 inches. Assume the standard deviation is known to be 1.3 inches.

Arandom sample of n = 25 observations is taken from a n(µ, σ ) population. a 95% confidence interval for µ was calculated to be (42.16, 57.84). the researcher feels that this interval is too wide. you want to reduce the interval to a width at most 12 units. a) for a confidence level of 95%, calculate the smallest sample size needed. b) for a sample size fixed at n = 25, calculate the largest confidence level 100(1 − α)% needed.