Question

A laboratory procedure is used to measure the level of cadmium in soil. It is applied to a specimen that has a controlled level of 1.5 μg/g of cadmium. Three measurements are obtained by splitting the specimen into three parts of equal weight and applying the procedure to each part. Here are the results: 1.64, 1.85, and 1.94. (a) Does a 95% confidence interval give an indication that the laboratory procedure may be biased? b. What are your assumptions that you are making to produce the confidence interval? second part of question: For 95% confidence interval of (1.38, 1.92) is given for the mean of a population based on the normal distribution. Re-express this as a 90% confidence interval

Answer 1

For part a)

When the sample is split into three parts, the CI equation has root n in the denominator which will become n/3 for each of the split samples. For constructing a confidence interval, we should take a sufficiently large n greater than 30. Assuming a sufficiently large n and then accounting for variation in measurements using standard deviation, we can create a good confidence interval so as to eliminate any bias that can arise out of the procedure.