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Population Proportion Estimation Considerations Quick Check
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Question
You want to demonstrate that the mean of the sampling distribution is approximately equal to the population proportion. You have two sets of data to use: one is a sample size of 75, and the other is a sample size of 400. Which of the following statements is true?(1 point)
Responses

The sample size of 400 will give a better approximation of population proportion, as it is symmetrical and the mean falls close to the middle of the distribution.
The sample size of 400 will give a better approximation of population proportion, as it is symmetrical and the mean falls close to the middle of the distribution.

The sample size of 400 will not give a better approximation of population proportion, as it has more variability and the mean falls close to the middle of the distribution.
The sample size of 400 will not give a better approximation of population proportion, as it has more variability and the mean falls close to the middle of the distribution.

The sample size of 75 will give a better approximation of population proportion, as it has more variability in the data and is less symmetric.
The sample size of 75 will give a better approximation of population proportion, as it has more variability in the data and is less symmetric.

The sample size of 75 will not give a better approximation of population proportion, as it has less variability in the data and is more symmetrical.
The sample size of 75 will not give a better approximation of population proportion, as it has less variability in the data and is more symmetrical.
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All Answers 1

Answered by GPT-5 mini AI
The correct choice is the one saying the sample size of 400 will give a better approximation of the population proportion, because the sampling distribution is more symmetric and has less variability (so the mean is close to the population proportion).

Reason: larger n reduces the standard error √[p(1−p)/n] and makes the sampling distribution more nearly normal (when np and n(1−p) are ≥10).