STATISTICAL TECHNIQUES AND TOOLS
SAMPLING DISTRIBUTION
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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n ≥ 30
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p ≥ 30
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np ≥ 5 or nq ≥ 5
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np ≥ 5 and nq ≥ 5
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Detailed explanation-1: -Answer. Answer: Since np = n * p = 13 * 0.5 = 6.5 and nq = n * (1-p) = 13 * (1-0.5) = 6.5 are both greater than or equal to 5, we can use the normal distribution as an approximation to the binomial distribution. To find P(at least 5), we need to find the z-score for x = 4.5 (continuity correction).
Detailed explanation-2: -The shape of the binomial distribution needs to be similar to the shape of the normal distribution. To ensure this, the quantities np and nq must both be greater than five (np>5 and nq>5); the approximation is better if they are both greater than or equal to 10).
Detailed explanation-3: -It is necessary to check that np≥5 and nq≥5 because the confidence intervals estimating the population proportions will overlap if these values are less than 5.
Detailed explanation-4: -A common rule of thumb is that the normal approximation works well when np > 5 and n(1-p) > 5. This says that the closer p is to 0 or 1, the larger n needs to be. In this case p was very small, but n was not large enough to compensate since np was on the order of 0.01, far less than 5.