Question

Suppose that n =100 random samples of water from a freshwater lake were taken and the calcium concentration (milligrams per liter) measured. A 95% CI on the mean calcium concentration is (0.49 ≤ µ ≤ 0.82). a) Would a 99% CI calculated from the same sample data be longer or shorter, explain your answer? b) Consider the following statement: There is a 95% chance that µ is between 0.49 and 0.82. Is this statement correct? Explain your answer. c) Given the information that the σ = 5.6, find the sample size needed to compute a 90% CI of width 2.3.

Answer 1

a)

Since confidence level increases to 99% from 95% , the aaccuracy for population mean to lie in

interval also increases.

For this reason the CI for 99% level would be longer

b)

correct Interpretation - We are 95% confident that is between 0.49 and 0.82

Given statement in question is not correct

c)

margin of error E = Width / 2 = 2.3 / 2 = 1.15

Sample size = (Z/2 * / E)2

= ( 1.6449 * 5.6 / 1.15)2

= 64.16

Sample size = 65 (Rounded up to nearest integer)