5.08 4.66 4.70 4.66 4.87 5.05 4.70 5.05 5.50 4.87 4.87 4.66 4.87 4.50 4.70 5.07

Question

5.08

4.66

4.70

4.66

4.87

5.05

4.70

5.05

5.50

4.87

4.87

4.66

4.87

4.50

4.70

5.07

4.87

4.66

4.60

Fish Toxins. A sample of 19 steelhead fish were caught in a lake to study the effects of the toxin diazinon on local fish populations. The weight in pounds of each fish is given below.

Research Problem: Use a 95% confidence interval to determine the median weight M of steelhead in the lake after being exposed to the toxin..

e) Before the effects of the toxin, the median weight of steelhead in the lake was 4.95 pounds. Is it believable that the population median of the fish exposed to the toxin could be ? Why or why not?

5.08

4.66

4.70

4.66

4.87

5.05

4.70

5.05

5.50

4.87

4.87

4.66

4.87

4.50

4.70

5.07

4.87

4.66

4.60

Explanation / Answer

The 95% confidence interval for median weight M is given by two values one lower limit and one upper limit

the 95% confidence intervals values will be

= n * 0.5 +- 1.96 * sqrt (0.5 * 0.5 * n)

= 19 * 0.5 +- 1.96 * sqrt(0.25* 19)

= 9.5 +- 4.27

= (5.23 , 13.77)

95% median interval would be 6 th and 14th value in ascending order.

Median = 487

6 th vaalue = 466

14th value = 487

so 95% confidence interval for median weight = (466, 487)

(e) The median weight of steelhead in the lake earlier before the effects of the toxin was 4.95 pounds. So, yes it is believable that the the fish are exposed to the toxin as their median weight has been reduced due to the effect of the toxin.

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