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 ≥ 10
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np and nq are both ≥ 10
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n ≥ 30 OR the population is normal
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np ≥ 10 AND the population is normal
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Detailed explanation-1: -The central limit theorem states that the sampling distribution of the mean will always follow a normal distribution under the following conditions: The sample size is sufficiently large. This condition is usually met if the sample size is n ≥ 30.
Detailed explanation-2: -The central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size gets larger, regardless of the population’s distribution. Sample sizes equal to or greater than 30 are often considered sufficient for the CLT to hold.
Detailed explanation-3: -*In Q2 we determined that there is a 99.8% chance that the mean of a sample of N=100 will be within 30 points of the population mean. Thus, the probability that a mean for a sample withN=100 will differ from the population mean by more than 30 points is 100% – 99.8%, or 0.2%.
Detailed explanation-4: -For samples of size 30 or more, the sample mean is approximately normally distributed, with mean ˉX= and standard deviation ˉX=/√n, where n is the sample size. The larger the sample size, the better the approximation.