RESEARCH METHODOLOGY

STATISTICAL TECHNIQUES AND TOOLS

SAMPLING DISTRIBUTION

Question [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
The average cost for a gallon of gasoline is $2.51 (source AAA.org) with a standard deviation of $0.42. Find the mean and standard error of the sampling distribution if n is decreased to 25.
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Explanation: 

Detailed explanation-1: -The standard deviation of the sampling distribution of means equals the standard deviation of the population divided by the square root of the sample size. The standard deviation of the sampling distribution is called the “standard error of the mean.”

Detailed explanation-2: -The central limit theorem says that the sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough. Regardless of whether the population has a normal, Poisson, binomial, or any other distribution, the sampling distribution of the mean will be normal.

Detailed explanation-3: -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.

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