STATISTICAL TECHNIQUES AND TOOLS
SAMPLING DISTRIBUTION
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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The mean distance an ASA student travels to school is 5.6 miles with a standard deviation of 1.7 miles. Is it more likely to find one student that travels more than 6 miles to school or a mean of a sample of 29 students that travel more than 6 miles?
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It is more likely to find 1 student that travels more than 6 miles to school
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It is more likely to find a sample of 29 students whose mean is greater than 6 miles
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Both equally likely
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There is not enough information to answer this question
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Explanation:
Detailed explanation-1: -(a) When N is 16, Mean==50Standard error=SE=√N=6√16=64=0.5. Hence, the standard deviation of the sample mean ( standard error) and the mean of this sample are computed as 1.5 and 50.
Detailed explanation-2: -For samples of any size drawn from a normally distributed population, the sample mean is normally distributed, with mean X= and standard deviation X=/√n, where n is the sample size.
Detailed explanation-3: -Regardless of the distribution of the population, as the sample size is increased the shape of the sampling distribution of the sample mean becomes increasingly bell-shaped, centered on the population mean.
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