Question

Three scientists want to estimate the mean weight of fish in the same lake. To do this, each scientist randomly chose 4 fish from the lake and recorded their weights. The samples are shown below. Do not round your answers.

Answer 1

SOLUTION:

Case: Averages

Method:

Sample 1

Mean

$\begin{gathered} m=\frac{3+3+7+4}{4} \\ m=4.25 \end{gathered}$

Sample 2

Mean

$\begin{gathered} m=\frac{6+3+8+2}{4} \\ m=\frac{19}{4} \\ m=4.75 \end{gathered}$

Sample 3

Mean

$\begin{gathered} m=\frac{2+4+8+5}{4} \\ m=\frac{19}{4} \\ m=4.75 \end{gathered}$

b) Range of sample means:

R = 4.75 - 4.25

R = 0.5

c)

The following statements are valid:

i) The closer the range of the sample mean is to 0. The more confident they can be in their estimate

iii) The mean of the sample mean will tend to be a much better estimate than a single sample mean.

Final answers:

a)

SAMPLE 1. m = 4.25

SAMPLE 2. m = 4.75

SAMPLE 3. m = 4.75

b) Range = 0.5

c)

i) The closer the range of the sample mean is to 0. The more confident they can be in their estimate

iii) The mean of the sample mean will tend to be a much better estimate than a single sample mean.