Choose the correct response. Why is sampling without replacement acceptable with a large population?
a. When a small sample is taken from a large population, the samples maintain their independence.
b. When a large sample is taken from a large population, the sample retains the characteristics of the original distribution.
c. When a sample without replacement is taken, there is no requirement to maintain the same sample size.
d. When a sample without replacement is taken, the samples will have the appropriate amount of data.
the answer is When a small sample is taken from a large population, the samples maintain their independence. i assure you it right ✌✌
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b. When a large sample is taken from a large population, the sample retains the characteristics of the original distribution. Because, you know, just like a good clone, you want your sample to closely resemble the original.
b. When a large sample is taken from a large population, the sample retains the characteristics of the original distribution.
The correct response is b. When a large sample is taken from a large population, the sample retains the characteristics of the original distribution.
Explanation:
Sampling without replacement means that once an item is selected from the population, it is not put back into the population before the next selection is made. This is typically done when the population is large compared to the sample size.
The reason why sampling without replacement is acceptable with a large population is that when a large sample is taken from a large population, the sample retains the characteristics of the original distribution. This means that the proportions, means, and other statistical properties of the population are well represented in the sample, allowing for accurate inference about the population.
Option a. is incorrect because the independence of samples is not related to the size of the population. Independence of samples is a property that primarily depends on the sampling method and design.
Option c. is incorrect because the requirement to maintain the same sample size does not depend on whether the sample is taken with or without replacement. The decision to maintain the same sample size is independent of the sampling method.
Option d. is incorrect because the appropriateness of the amount of data in the sample does not depend on the sampling method used. The adequacy of the sample size depends on the research question, desired level of precision, and statistical power, among other factors.