Asked by Claire Liang on Jun 25, 2024
Verified
As a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever
A) np ≥5, n ≥30.
B) np ≥5 and n(1-p) ≥5.
C) n 30 and (1 - p) = 0.5.
D) none of these alternatives is correct.
Normal Probability Distribution
A symmetric, bell-shaped distribution that is characterized by its mean and standard deviation, representing the distribution of many types of data.
Rule of Thumb
A broadly applicable guideline or an easy generalization that is not necessarily very accurate but useful for making approximate judgments.
- Absorb the idea and relevance of standard error in deducing statistical conclusions.
- Understand the effects of varying probabilities on the standard error of proportions.
Verified Answer
HT
Haleigh TarmanJun 28, 2024
Final Answer :
B
Explanation :
The rule of thumb for approximating the sampling distribution of sample proportions with a normal distribution is np≥5 and n(1-p)≥5. This ensures that there are a sufficient number of successes and failures in the sample, which allows for an accurate approximation of a normal distribution. Additionally, choice A includes n≥30 as a requirement, which is not always necessary for an accurate approximation. Choice C requires (1-p) to be exactly 0.5, which is not always the case in real-world situations. Choice D suggests that none of the alternatives are correct, which is not true as choice B satisfies the necessary conditions for the approximation.
Learning Objectives
- Absorb the idea and relevance of standard error in deducing statistical conclusions.
- Understand the effects of varying probabilities on the standard error of proportions.
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