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Which of the following statement is NOT true about sample size?

a. Having a large sample size allows us to assume our response has a normal distribution
b. Having a large sample size helps to ensure that we have complete information requirement.
c. Having a large sample size helps us to guarantee a stable solution
d. Having a large sample size allows us to assume our coefficients have a normal distribution

1 Answer

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Final answer:

The untrue statement about sample size is that it ensures complete information. A larger sample size allows assumptions of normality but does not guarantee completeness or stability of the information or the solution.

Step-by-step explanation:

The statement that is NOT true about sample size is "Having a large sample size helps to ensure that we have complete information requirement." While a large sample size can provide a more reliable estimate of a population parameter and can, due to the Central Limit Theorem, allow for the assumption that our response and coefficients will have a normal distribution assuming the sample size is large enough (typically n ≥ 30), it does not guarantee that the information is complete or that the solution is stable. A large sample size reduces sampling variability and makes for a better, more reliable statistic, but it cannot ensure completeness because the quality of data and sampling technique is also essential. Furthermore, if the sampling method is biased, even a large sample size would not make the sample representative of the population. Therefore, option (b) "Having a large sample size helps to ensure that we have complete information requirement." is the incorrect statement about sample size.

User Dalbir Singh
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