The sample mean to be calculated from a random sample of size n= 4 from a population consists of eight measurements (2, 6, 9, 12, 25, 29, 39, 50) . find the sampling distribution of y .(Hint : there are 70 samples of size 4 when sampling from a population of eight measurements )
To find the sampling distribution of y, which is the sample mean, we need to calculate the mean for all possible samples of size 4 taken from the population. Here's how you can do it:
Step 1: Write down all possible combinations of four measurements from the given data set. There are 70 different combinations possible when sampling from a population of eight measurements.
Step 2: Calculate the mean for each of these combinations. To do this, add up the four measurements in each combination and then divide the sum by 4 (since we have a sample size of 4).
For example, let's calculate the mean for the first combination: (2, 6, 9, 12)
Mean = (2 + 6 + 9 + 12) / 4 = 29 / 4 = 7.25
Repeat this step for all 70 combinations, and you will have the sample means for each combination.
Step 3: Now, you have a set of 70 sample means. This set represents the sampling distribution of y. This distribution will give you an idea of how the sample means are distributed around the population mean.
Note: In this case, the population mean is not given, so we cannot make any comparison between the sampling distribution and the population mean. However, in general, the sampling distribution of the sample mean is expected to have a mean close to the population mean and a narrower spread as the sample size increases.
By following these steps, you can find the sampling distribution of y for the given data.