Respuesta :
a. Population mean:
To find the population mean, we sum up all the numbers in the population and divide by the total number of elements:
Population mean = (2 + 4 + 6) / 3 = 12 / 3 = 4
b. Population variance:
To find the population variance, we need to calculate the squared differences between each element and the population mean, then divide by the total number of elements:
Population variance = [(2 - 4)^2 + (4 - 4)^2 + (6 - 4)^2] / 3 = (4 + 0 + 4) / 3 = 8 / 3
c. Population standard deviation:
Population standard deviation is the square root of the variance:
Population standard deviation = √(8 / 3)
d. List all the sample sizes of 2 without replacement:
All possible combinations of 2 elements without replacement from the population {2, 4, 6} are:
(2, 4), (2, 6), (4, 2), (4, 6), (6, 2), (6, 4)
e. Mean of the sampling distribution of means:
The mean of the sampling distribution of means is equal to the population mean, which is 4.
f. Variance of the sampling distribution of means:
Since we are sampling without replacement, the variance of the sampling distribution of means (also known as the variance of the sampling distribution of sample means) can be calculated using the formula for the variance of a sampling distribution:
Variance of sampling distribution of means = Population variance / Sample size
Variance of sampling distribution of means = (8 / 3) / 2 = 4 / 3
g. Standard deviation of the sampling distribution of means:
The standard deviation of the sampling distribution of means is the square root of the variance of the sampling distribution of means:
Standard deviation of sampling distribution of means = √(4 / 3)
These values provide insights into the population and its sampling distributions under the given conditions.
