Question

Suppose that a laboratory analyzes biological specimens to determine the concentration of toxins. The laboratory analyzes each specimen five times and reports the mean results. The five measurements for a given specimen are not all equal, but the results follow a normal distribution almost exactly. Assume the mean of the population of all repeated measurements, μ , is the true concentration in the specimen. The standard deviation of this distribution is known to be 0.2000 ppm. One of the laboratory’s technicians evaluates the claim that the concentration of toxins in a single specimen is at most 6.350 ppm using a one-sample z ‑test for a mean. The true concentration is the mean, μ , of the population of repeated analyses. H 0 : μ = 6.350 ppm H 1 : μ > 6.350 ppm The technician conducts his test at a significance level of 5%. First, determine the minimum value of the sample mean, ¯ x , for which the technician will reject the null hypothesis. You may find a table of critical values from the standard normal distribution or some software manuals helpful. Round your answer to three decimal places. What is the power of the technician's test to reject the null hypothesis if the mean concentration is really μ = 6.550 ppm? Give your answer precise to at least two decimal places. ¯ x = ppm power =

Answer 1