Question

In August 2013, radioactive water from the damaged Fukushima Daiichi nuclear plant leaked into the Pacific Ocean. The contaminated groundwater seeped through an underground barrier created through chemical injections, and the Japanese Nuclear Regulatory Authority declared an emergency. In response, Tepco (the plant's operator) began pumping out more groundwater to ease the spill into the ocean. Concentrations of cesium-137 (in Bq/l) in the seawater 10 - 30 kilometers off the Japanese coast were taken at eight different locations one week apart, before and after the additional pumping. The data are given in the following table. Location 1 2 3 4 5 6 7 8 August 23 16.0 12.0 14.0 18.0 12.0 12.5 10.5 15.5 August 30 16.0 9.0 11.0 16.0 14.0 8.5 6.5 14.5 At a = 0.05 is there any evidence to suggest that the population mean cesium-137 level decreased from August 23 to August 30? State the assumption(s) required for the test

Answer 1

$\bar d$ = (0 + 3 + 3 + 2 + (-2) + 4 + 4 + 1)/8 = 1.875

s_d = sqrt(((0 - 1.875)^2 + (3 - 1.875)^2 + (3 - 1.875)^2 + (2 - 1.875)^2 + (-2 - 1.875)^2 + (4 - 1.875)^2 + (4 - 1.875)^2 + (1 - 1.875)^2)/7) = 2.1

$H_{0}: \mu_{d} \leq 0$

$H_{1}: \mu_{d} > 0$

The test statistic is

t= d-D sa/n

$= \frac{1.875 - 0}{2.1/\sqrt 8}$

  

df = 8 - 1 = 7

At $\alpha$ = 0.05, the critical value is t_{0.05, 7} = 1.895

Since the test statistic value is greater than the critical value (2.525 > 1.895), so we should reject the null hypothesis.

At 0.05 significance level, there is sufficient evidence to conclude that the population mean cesium-137 level decreased from August 23 to August 30.

We should assume that population is normally distributed from which the samples are drawn.