population consists of six numbers 1, 2, 3, 4, 6, 8. Consider all samples of size
two which can be drawn without replacement from this population.
i. The mean of the sampling distribution of means.
ii. The standard deviation of the sampling distribution of mear
i. To find the mean of the sampling distribution of means, we need to first find all possible samples of size two that can be drawn without replacement from the population of 1, 2, 3, 4, 6, 8.
The possible samples are:
1, 2
1, 3
1, 4
1, 6
1, 8
2, 3
2, 4
2, 6
2, 8
3, 4
3, 6
3, 8
4, 6
4, 8
6, 8
Next, we calculate the mean of each sample:
(1+2)/2 = 1.5
(1+3)/2 = 2
(1+4)/2 = 2.5
(1+6)/2 = 3.5
(1+8)/2 = 4.5
(2+3)/2 = 2.5
(2+4)/2 = 3
(2+6)/2 = 4
(2+8)/2 = 5
(3+4)/2 = 3.5
(3+6)/2 = 4.5
(3+8)/2 = 5.5
(4+6)/2 = 5
(4+8)/2 = 6
(6+8)/2 = 7
Now we find the mean of these means:
(1.5 + 2 + 2.5 + 3.5 + 4.5 + 2.5 + 3 + 4 + 5 + 3.5 + 4.5 + 5.5 + 5 + 6 + 7) / 15 = 4.1
Therefore, the mean of the sampling distribution of means is 4.1.
ii. To find the standard deviation of the sampling distribution of means, we first need to calculate the variance of the sampling distribution.
Variance = (sum of (sample mean - mean of sampling distribution of means)^2) / (number of samples)
((1.5-4.1)^2 + (2-4.1)^2 + ... + (7-4.1)^2) / 15 = 3.02
Standard deviation = square root of variance = √3.02 = 1.74
Therefore, the standard deviation of the sampling distribution of means is 1.74.