Mercury is a heavy metal that can cause severe health problems in even small concentrations. Fish and shellfish efficiently concentrate mercury into their flesh, so it is important to monitor seafood for its mercury Content.
An extensive study conducted in 1980 concluded that the mean mercury level in oysters from the White Bear Estuary was 0.021 parts per million (ppm) with a standard deviation $\sigma = 0.032 \text { ppm }$ In 2012, a Sample of 47 oysters from the same estuary exhibited a mean mercury concentration of 0.017 ppm.
Can you conclude that the 2012 mercury concentration is lower than in 1980? Use the $\alpha = 0.05$ level of
Significance.
A) No. There is insufficient evidence to conclude that the mercury concentration has decreased from 1980 to 2012.
B) Yes. The mercury concentration appears to be lower in 2012.
C) There is not enough information to reach a conclusion.

Question

Quizplus · Accepted Answer

To determine if there is significant evidence that the mercury concentration has decreased from 1980 to 2012, we need to perform a hypothesis test. Let μ1 be the mean mercury concentration in 1980 and μ2 be the mean concentration in 2012.

Null Hypothesis: μ1 = μ2 
Alternative Hypothesis: μ1 > μ2

We choose a one-tailed test because we are only interested in detecting a decrease in mercury concentration.

Using a t-test with 46 degrees of freedom, we find the t-statistic to be: 
t = (0.021 - 0.017) / (0.032 / sqrt(47)) = 1.65

At the α = 0.05 level of significance with a one-tailed test, the critical t-value is 1.677. Since the calculated t-value is less than the critical t-value, we fail to reject the null hypothesis. Therefore, there is insufficient evidence to conclude that the mercury concentration has decreased from 1980 to 2012.

Mercury Is a Heavy Metal That Can Cause Severe Health σ=0.032 ppm \sigma = 0.032 \text { ppm }σ=0.032 ppm

Mercury Is a Heavy Metal That Can Cause Severe Health $\sigma = 0.032 \text { ppm }$