Question

In a sample of n=13 lichen specimens, the researchers found the mean and standard deviation of the amount of the radioactive element, cesium137 , that was present to be 0.009 and 0.006 microcurie per milliliter, respectively. Suppose the researchers want to increase the sample size in order to estimate the mean μ to within 0.001 microcurie per milliliter of its true value, using a 95% confidence interval. Complete parts a through c.

a. What is the confidence level desired by the researchers? The confidence level is

Answer 1

The researchers are aiming for a 95% confidence level to estimate the mean amount of cesium137 within 0.001 microcurie per milliliter of its true value.

Step-by-step explanation:

The confidence level desired by the researchers is 95%. This is because they have specified that they want to estimate the mean μ to within 0.001 microcurie per milliliter of its true value using a 95% confidence interval. To achieve the narrower margin of error of 0.001 microcurie per milliliter at the same confidence level, they would need to increase their sample size. The exact sample size needed can be calculated using the formula for the margin of error in a confidence interval, which is based on the standard deviation, the desired confidence level (which reflects the Z-score), and the desired margin of error.