STATISTICAL TECHNIQUES AND TOOLS
SAMPLING DISTRIBUTION
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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Which of the following pairs of sample size n and population proportion p would produce the greatest standard deviation for the sampling distribution of a sample proportion p?
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n = 1, 000 and p close to 0
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n = 1, 000 and p close to 1
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n = 1, 000 and p close to 1/2
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n = 100 and p close to 0
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n = 100 and p close to 1/2
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Explanation:
Detailed explanation-1: -The sampling distribution of p is approximately normally distributed if N is fairly large and is not close to 0 or 1. A rule of thumb is that the approximation is good if both N and N(1-) are greater than 10.
Detailed explanation-2: -In an SRS of size n, what is true about the sampling distribution of when the sample size n increases? As n increases the sampling distribution of becomes approximately normal.
Detailed explanation-3: -The mean of the distribution of the sample proportions, denoted ^p, equals the population proportion. ^p=p. The standard deviation of the of the sample proportions (called the standard error of the proportion), denoted ^p, is. ^p=√p×(1−p)n.
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