(7 points) 4. A marine biologist is interested in estimating the mean length of salmon in the Rogue River. She wants to use a 97% confidence level and she knows the population standard deviation is 10 inches. (a) What size random sample should she take for each possible desired margin of error given in the following table? Recall: The formula for determining necessary sample size is n = (zalzo ) . See page 53 of the workbook. Desired Necessary Sample Size Margin of Error 3 inches For a 3 inch margin of error, the necessary sample size is n = [(2.17)(10)12 3 52.11. Thus, the biologist must sample 53 salmon to construct a confidence interval with a 3-inch margin of error. 2 inches 1 inch 0.5 inch (b) What happens to the necessary sample size as the desired margin of error decreases? Use clear, complete sentences to state and justify your answer. Hint: Look at your answer to part (a). 6