Answer
(a)
Sample | Mean
1 | 4.75
2 | 4.75
3 | 4.25
(b) range of sample means = 0.5
(c) The closer the range of sample means is to 0, the more confident they can be in their estimate.
The mean of sample means will tend to be a better estimate than a single sample mean
Step-by-step explanation
(a) Mean is calculated with the next formula:
[tex]mean=\frac{sum\text{ of the terms}}{number\text{ of terms}}[/tex]Considering Sample 1, its mean is:
[tex]\begin{gathered} mean_1=\frac{6+5+2+6}{4} \\ mean_1=\frac{19}{4} \\ mean_1=4.75 \end{gathered}[/tex]Considering Sample 2, its mean is:
[tex]\begin{gathered} mean_2=\frac{4+8+4+3}{4} \\ mean_2=\frac{19}{4} \\ mean_2=4.75 \end{gathered}[/tex]Considering Sample 3, its mean is:
[tex]\begin{gathered} mean_3=\frac{5+4+2+6}{4} \\ mean_3=\frac{17}{4} \\ mean_3=4.25 \end{gathered}[/tex](b) Range is calculated with the next formula:
[tex]range=maximum\text{ value }-minimum\text{ value}[/tex]From the previous results, the range of the sample means is:
[tex]\begin{gathered} range\text{ }of\text{ }sample\text{ }means=4.75-4.25 \\ range\text{ o}f\text{ s}ample\text{ m}eans=0.5 \end{gathered}[/tex](c) The closer the range of sample means is to 0, the more confident they can be in their estimate. If this range is near zero, then the mean of sample means will be closer to every single sample mean, and then the estimate is better.
The mean of sample means will tend to be a better estimate than a single sample mean. This is because the mean of sample means takes into consideration more data than a single sample mean.