Question

A county environmental agency suspects that the fish in a particular polluted lake have elevated mercury levels. To confirm that suspicion, five striped bass in that lake were caught and their tissues tested for the presence of mercury. For the purposes of comparison, four striped bass in an unpolluted lake were also caught and tested. The fish tissue mercury levels in mg/kg are given below. (Note: You may wish to use Excel for this problem.)

Sample 1 (polluted lake) 0.580, 0.711, 0.571, 0.666, 0.598

Sample 2 (unpolluted lake) 0.382 0.276 0.570 0.366

a. Construct the 95% confidence interval for the difference in the population means based on these data.

b. Test, at the 0.05 significance level, whether the data provide sufficient evidence to conclude that fish in the polluted lake have elevated levels of mercury in their tissue.

c. Do your answers to (a) and (b) agree or disagree? Explain.

Answer 1

	Polluted Lake	Unpolluted lake
Mean	0.6252	0.3985
Variance	0.0037	0.0152
Observations	5	4
Hypothesized Mean Difference	0
df	4

a)
t-value = 2.7764
SE = sqrt(0.0037/4 + 0.0152/5) = 0.0630

CI = (0.6252 - 0.3985 - 2.7764*0.0630, 0.6252 + 0.3985 + 2.7764*0.0630)

= (0.0518, 0.4016)

b)
Test statistic,
t = (0.6252 - 0.3985)/0.0630 = 3.3610

p-value = 0.0141

As p-value is less than significance level of 0.05, reject H0

c)
(a) and (b) agree with each other
As 0 is not included in the CI, we reject H0