Question

Question 10 (1 point)
A county environmental agency suspects that the fish in a particular polluted lake have elevated mercury level. To confirm that suspicion, five striped bass in that lake were caught and their tissues were tested for mercury. For the purpose 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.

polluted: 0.580, 0.711, 0.571, 0.666, 0.598
unpolluted: 0.382, 0.276, 0.570, 0.366

Construct the 90% confidence interval for the difference in the population means based on these data.

Question 10 options:

0.05 to 0.40

0.08 to 0.37

0.10 to 0.35

0.04 to 0.41

Answer 1

Solution

The formula for estimation is:

μ1 - μ2 = (M1 - M2) ± ts(M1 - M2)

where:

M1 & M2 = sample means
t = t statistic determined by confidence level
s(M1 - M2) = standard error = √((s2p/n1) + (s2p/n2))

Calculation

Pooled Variance
s2p = ((df1)(s21) + (df2)(s22)) / (df1 + df2) = 0.06 / 7 = 0.01

Standard Error
s(M1 - M2) = √((s2p/n1) + (s2p/n2)) = √((0.01/5) + (0.01/4)) = 0.06

Confidence Interval
μ1 - μ2 = (M1 - M2) ± ts(M1 - M2) = 0.2267 ± (1.89 * 0.06) = 0.2267 ± 0.118149

0.10 <μ1 - μ2 <0.35

the 90% confidence interval for the difference in the population means based on these data

0.10 to 0.35