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Answer :
Final answer:
It's essential to check the large counts condition to ensure the applicability of the normal approximation to the sampling distribution of the sample proportion, p. This involves verifying that both the number of successes and failures in the sample are sufficiently large. Meeting these criteria allows for the proper use of normal distribution in statistical inference.
Explanation:
Importance of Checking Large Counts Condition
When dealing with sampling distributions of the sample proportion, p, it is crucial to check the large counts condition. This condition states that for the sampling distribution of the sample proportion to be approximated well by a normal distribution, both of the following quantities must be large enough:
- np (number of successes) should be greater than or equal to 10
- n(1 - p) (number of failures) should also be greater than or equal to 10
This ensures that the total number of successes and failures has a sufficient number of counts to allow for the normal approximation to be applied. If the large counts condition is satisfied, it leads to the ability to use the standard deviation formula for the sampling distribution of p accurately and supports using the normal distribution for inference.
Therefore, to directly answer the question, the correct answer is D: To ensure that the usage of the normal approximation is appropriate.
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