hellooo, can i please get help with these stat questions because i am very confu
ID: 3324168 • Letter: H
Question
hellooo, can i please get help with these stat questions because i am very confused and i have a very horrible statistics professor :^((((
Example Small population: 3, 6, 9, 12, 15 (N-5 Sample size n = 3 (without replacement) ndom sample drawn from 5 distinct numbers: X 3,6,9,12,15 probability P(x) (equally likely) Mean -(3 + 6 + 9 + 12 + 15)/5-9 Median M=9 (3,6,9, 12,15) There are 5C, 10 possible random samples of size n=3 (from a population 5) and are equally likely, with probability 1/10 SampleNumber1 4 /Sample Valu s l56,913 6,12 3,6,15 3 9 123,9, 151.3 12,1 516,9,1216 9,15 612.15 2,15 9 10 10 12 Sample mean x Sample median m Sampling Distribution for Sample Mean x 10 Sampling Distribution for Sample Median m 12 = 0.3 p(m) 0.3 = 0.4 (For large population size and large sample size, use a simulation(s) to approximate the sampling distribution empirically) population mehw n30Explanation / Answer
Hi,
I think the question is more to do with proving right the fact that the mean of the sampling distribution is equal to the population mean.
So, IN the first part the mean is calculated as 9, which is essentially the population mean
Now, we are taking 3 out the 5 at random and taking out mean of each of 5C3 = 10 samples, then take out the expected value of the means all the samples to get the sample mean.
hence, the first box describes the mean of each of the 10 samples
And the 2nd box calcutes probability of each sample to occur.
So, the expected value is .1*6+7*.1+8*.2+9*.2+10*.2+11*.1+12*.1 = 9
And the population mean is (3+6+9+12+15) = 9
So, Sample mean = Population Mean. And this is what central limit theroem postulates - it says that sample mean of the sampling distriution will be same as population mean. The same goes for the sampling median.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.