Question

Population: X= {4, 5, 6, 6}
Determine the sampling distribution of the mean for random samples of two from population X

Answer 1

To determine the sampling distribution of the mean for random samples of two from population X, we need to calculate all possible combinations of two elements from the population X and calculate the mean for each combination.

The population X is {4, 5, 6, 6}.

The possible combinations of two elements are:
- (4, 5)
- (4, 6)
- (4, 6)
- (5, 6)
- (5, 6)
- (6, 6)

Now, we calculate the mean for each combination:
- For (4, 5): (4 + 5) / 2 = 4.5
- For (4, 6): (4 + 6) / 2 = 5
- For (4, 6): (4 + 6) / 2 = 5
- For (5, 6): (5 + 6) / 2 = 5.5
- For (5, 6): (5 + 6) / 2 = 5.5
- For (6, 6): (6 + 6) / 2 = 6

Therefore, the sampling distribution of the mean for random samples of two from population X is {4.5, 5, 5, 5.5, 5.5, 6}.