Question

Each of the 10,000 shelves in a certain library is 300 cm long. To estimate how many books in the library need rebinding, a librarian takes a sample of 50 books using the following procedure: He first generates a random integer between 1 and 10,000 to select a shelf, and then generates a random number between 0 and 300 to select a location on that shelf. Thus, the pair of random numbers (2531, 25.4) would tell the librarian to include the book that is above the location 25.4 cm from the left end of shelf number 2531 in the sample. Does this procedure generate an SRS of the books in the library? Explain why, or why not.

Answer 1

Answer:

If all the books are of the same size, this is truly a simple random sampling method.

If not, the random selection of the length of shelf at which the book to be sampled will be picked favours the bigger/fatter books and the process seizes to be a simple random sampling.

Check the explanation for more clarification.

Step-by-step explanation:

In simple random sampling, each member of the population has an equal chance of being sampled. The best way to go about this is usually to truly randomize the sampling technique by assigning numbers to members of a population and randomly picking the numbers. Any member of the population that the number picked belongs to, is picked to be sampled. The best way to pick random numbers is to use a computer program to do it these days.

So, for this problem, the librarian tries as much as possible and does randomize the sampling process enough for the books. But this is indeed a simple random sampling method if all the books truly have equal chance of being selected.

In selecting the shelf, it is as random as possible, but in selecting the book, the random length on the shelf picked will represent random sampling if all the books are similar in size. If not, the bigger/fatter books have a higher chance of being selected than the thinner ones and this seizes to be a random sampling technique if all the books do not have equal chance of being picked.