Answer:
When a sample is taken from a large population without replacement, the probability of selecting the same individual twice is very small compared to the total population size. As a result, the effect of the sample on the population is negligible and can be considered as independent events. In other words, the first sample selected does not affect the probability of selecting a particular individual in the subsequent samples, and the composition of the population remains largely unaffected.
Furthermore, when a large sample is taken from a large population, the Central Limit Theorem applies, which states that the sample mean will be approximately normally distributed, regardless of the population distribution, as long as the sample size is sufficiently large. Therefore, the sample will still retain the characteristics of the original population distribution, even if it is sampled without replacement.
Regarding the sample size, when a sample is taken without replacement, the sample size will still be the same as the number of individuals selected, as there is no replacement of individuals in the sample. However, the sample size may affect the precision and accuracy of the estimates obtained from the sample, as smaller samples may have higher sampling error.
In summary, sampling without replacement is acceptable with a large population because the probability of selecting the same individual twice is very small, and the sample will retain the characteristics of the original population distribution, provided the sample size is sufficiently large.
Step-by-step explanation: