Question

Suppose you work for the Department of Natural Resources and you want to estimate, with 95% confidence, the mean length of all walleye fingerlings in a fish large hatchery pond.  The pond contains several thousand fingerlings.  From a random sample of 36 fingerlings, the mean length is 19.30 cm with a standard deviation of 5.4 cm.

1. Calculate a 95% confidence interval for the true mean length of all fingerlings in the pond.  Include all the steps:  State the inference procedure, check the conditions, perform the calculations, and interpret the confidence interval.
2. Interpret the confidence LEVEL.
3. How many fingerlings need to be sampled in order to estimate the true mean length to within 0.5 cm with the same level of confidence.  Show the calculations.

Answer 1

t value for 95% CI is TINV(0.05,35)=2.030

Hence Margin of Error is

Hence CI is

Population mean will lie in the range of 17.473 to 21.127 with 95% confidence

Now for E=0.5,