Given the population 2, 3, 6, 8, 11, N=5, n=2, sampling with replacement, calculate the population mean, population standard deviation, and the mean of the sampling distribution of means.

Here are the solutions to your questions: The population consists of the numbers 2, 3, 6, 8, 11. The population size is N = 5. The sample size is n = 2. Sampling is done with replacement. i) The mean of the population () Step 1: Sum all the values in the population. x = 2 + 3 + 6 + 8 + 11 = 30 Step 2: Divide the sum by the number of values in the population (N). = ( x)/(N) = (30)/(5) = 6 The mean of the population is 6. ii) The standard deviation of the population () Step 1: Calculate the squared difference between each population value and the population mean (=6). (x - )^2 (2 - 6)^2 = (-4)^2 = 16 (3 - 6)^2 = (-3)^2 = 9 (6 - 6)^2 = (0)^2 = 0 (8 - 6)^2 = (2)^2 = 4 (11 - 6)^2 = (5)^2 = 25 Step 2: Sum these squared differences. (x - )^2 = 16 + 9 + 0 + 4 + 25 = 54 Step 3: Divide the sum by the population size (N) and take the square root. = sqrt(( (x - )^2)/(N)) = sqrt((54)/(5)) = sqrt(10.8) ≈ 3.286 The standard deviation of the population is 3.29. iii) The mean of the sampling distribution of means (_x) Step 1: For sampling with replacement, the mean of the sampling distribution of means is equal to the population mean. _x = _x = 6 The mean of the sampling distribution of means is 6. iv) The standard deviation of the sampling distribution of means (_x) Step 1: Use the formula for the standard error of the mean for sampling with replacement. _x = ()/(sqrt(n)) Where = sqrt(10.8) (from part ii) and n = 2. _x = sqrt(10.8)sqrt(2) = sqrt((10.8)/(2)) = sqrt(5.4) _x ≈ 2.324 The standard deviation of the sampling distribution of means is 2.32. What's next?