Question

eldrick manages wildlife samples for ducks unlimited. two samples of duck populations at a migratory site are shown in the table below. which statement about the samples is true? duck pond samples sample 1 sample 2 mallard 21 mallard 8 wood duck 4 wood duck 17 green wing teal 9 green wing teal 15 american widgeon 6 american widgeon 0 eldrick can use both of these samples to find the mean frequency of each duck. eldrick should take another sample because there is too much variability in the two samples. eldrick should use only the first sample to find the mean frequency of each duck. eldrick should use only the second sample to find the mean frequency of each duck.

Explanation:

Step1: Calculate total of each sample

Sample 1 total: $21 + 4 + 9 + 6 = 40$
Sample 2 total: $8 + 17 + 15 + 0 = 40$

Step2: Analyze sample variability

Compare relative frequencies:

• Mallard: $\frac{21}{40}=0.525$ (Sample1), $\frac{8}{40}=0.2$ (Sample2)
• Wood Duck: $\frac{4}{40}=0.1$ (Sample1), $\frac{17}{40}=0.425$ (Sample2)
• Green Wing Teal: $\frac{9}{40}=0.225$ (Sample1), $\frac{15}{40}=0.375$ (Sample2)
• American Widgeon: $\frac{6}{40}=0.15$ (Sample1), $\frac{0}{40}=0$ (Sample2)

Large differences in relative frequencies show high variability.

Step3: Evaluate each option

• Option1: Combining highly variable samples gives unreliable mean frequencies. False.
• Option2: High variability means current samples are not representative; a new sample is needed. True.
• Option3: Using only Sample1 ignores the conflicting data from Sample2, which is not rigorous. False.
• Option4: Using only Sample2 ignores valid data from Sample1 and the 0 value for Widgeon is an outlier in this sample. False.

Answer:

Eldrick should take another sample because there is too much variability in the two samples.