Question

Radioactive cesium is a waste product of nuclear reactors. A study examined the tissue concentration of radioactive cesium in a random sample of 15 Pacific bluefin tuna captured off the coast of California four months after Fukushima (Japan) nuclear reactor meltdown of 2011. Here are the findings, in becquerels per kilogram of dry tissue (Bq/kg):

4.6 6.9 7.9 8.0 8.0 9.2 10.4 10.6 11.1 11.1 11.3 12.3 12.7 14.2 15.6

(a) Give a 95% confidence interval for the mean tissue concentration of radioactive cesium in bluefin tuna off the coast of California four months after the 2011 nuclear meltdown. Provide a full interpretation of the confidence interval.

(b) Historically, radioactive cesium tissue concentrations in bluefin tuna have been below 2 Bg/kg, on average. Use your confidence interval to compare the radioactive cesium levels after the 2011 nuclear meltdown with the historical average.

Answer 1

a)
sample mean, xbar = 10.26
sample standard deviation, s = 2.8911
sample size, n = 15
degrees of freedom, df = n - 1 = 14

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.145

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (10.26 - 2.145 * 2.8911/sqrt(15) , 10.26 + 2.145 * 2.8911/sqrt(15))
CI = (8.66 , 11.86)
Therefore, based on the data provided, the 95% confidence interval for the population mean is 8.66 < μ < 11.86 which indicates that we are 95% confident that the true population mean μ is contained by the interval (8.66 , 11.86)

b)
The calculated CI does not include 2, the radioactive cesium levels has increased significantly after the 2011 nuclear meltdown