simple random sampling with or without replacement?

Question

Is it right to understand that simple random sampling can be with or without replacement, but that the observations are only independent with replacement?

I have 2 statements in my textbook...

a) If the unit is not replaced this is sampling without replacement and this is simple random sampling.

b) Take a sample of n independent observations (sampling should be with replacement to ensure independence).

Does this mean that the lottery,which is a simple random sample without replacement, is a simple random sample, but the observations are not independent?

Answer 1

True. Sampling without replacement changes the population statistics every time you draw the sample. Therefore if the goal is to conclude about statistics of the original population the sampling should be without replacement. For example take that you have 100 socks 30% white and 70% black and you want to conclude how many are white by taking samples of 10. After taking the first sample consisting, say, of 5 white and 5 black socks without replacement the remaining population will be 25 whites and 65 black. The remaining population has 17.78 % white socks therefore is different from the original population. Therefore If you draw the second sample it will not represent original population.

Answer 2

the respond is B, and for the reason that of this. at first, you have 50 tickets, and 25 of them ar over 25, so your odds of pulling a intense fee fee ticket on the 1st pull are 25:50, or a million:2. Now on the 2d pull there are 40 9 tickets left and 24 intense ones (on account which you already pulledf a intense one. Your superb on the 2d pull are 24:40 9, and mixing that with the probabilities of the 1st pull, your odds of pulling 2 right now intense numbers is 24/ninety 8. The third pull has 40 8 tickets left and 23 of them are extra useful than 25, so your odds listed authentic listed right here are 23:40 8, which on a similar time as blended with different 2 pulls, makes your total odds 552:4704, which simplifies authentic right down to 23/196.

Answer 3

http://en.wikipedia.org/wiki/Simple_random_sample