Question
Draw a random sample of size $5$ $(i)$ with replacement $(ii)$ without replacement from a population of $50$ units using the following $15$ two digit random numbers: $62, 25, 6, 60, 95, 55, 98, 11, 71, 25, 20, 45, 89, 27, 40$
✓
Answer
We shall first assign numbers $1$ to $50$ to the $50$ units of the the population.
Since the size of the population is $50$ , we shall ignore random numbers which are greater than $50$ . So we are left with random numbers : $25,6,11,25,20,45,27$ and $40$ .
$(i)$ As the sample has to be selected with replacement, we shall not ignore the random numbers which are repeated more than once. As we require random sample of size $5$ , we shall select first $5$ random numbers. The selected random numbers are: $25,6,11,25$, and $20$.
$(ii)$ As the sample has to be selected without replacement, we shall ignore the random numbers are repeated more than once. As we require raddom sample of size $5$ , we shall select first $5$ random rs. The selected random numbers are: $25,6,11,20$, and $45$ . (as $25$ cannot be selected again)
Since the size of the population is $50$ , we shall ignore random numbers which are greater than $50$ . So we are left with random numbers : $25,6,11,25,20,45,27$ and $40$ .
$(i)$ As the sample has to be selected with replacement, we shall not ignore the random numbers which are repeated more than once. As we require random sample of size $5$ , we shall select first $5$ random numbers. The selected random numbers are: $25,6,11,25$, and $20$.
$(ii)$ As the sample has to be selected without replacement, we shall ignore the random numbers are repeated more than once. As we require raddom sample of size $5$ , we shall select first $5$ random rs. The selected random numbers are: $25,6,11,20$, and $45$ . (as $25$ cannot be selected again)
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