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 sampling distribution of x̄ has mean equal to the population mean
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The sampling distribution of x̄ has standard deviation / √n even if the population is not normally distributed.
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The sampling distribution of x̄ is normal if the population has a normal distribution.
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When n is large, the sampling distribution of x̄ is approximately normal even if the population is not normally distributed.
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The larger the value of the sample size n, the closer the standard deviation of the sampling distribution of x̄ is to the standard deviation of the population.
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Detailed explanation-1: -Standard error decreases when sample size increases – as the sample size gets closer to the true size of the population, the sample means cluster more and more around the true population mean.
Detailed explanation-2: -However, the variability in the sample means will depend on the size of the samples, since larger samples are more likely to give estimated means that are closer to the true mean of the population.
Detailed explanation-3: -For a variable x and a given sample size n, the distribution of the variable x̅(all possible sample means of size n) is called the sampling distribution of the mean. Note: The larger the sample size the smaller the sampling error tends to be in estimating a population mean, , by a sample mean x̅.