Answer the following questions: A. In general, what data make up a distribution
ID: 3216787 • Letter: A
Question
Answer the following questions: A. In general, what data make up a distribution of raw scores? What does each data point represent? B. In general, what data make up a sampling distribution of the mean? What does each data point represent? C. Suppose you have three standard deviations, all derived from the same population: the standard deviation of a population of raw scores, the standard deviation of a sample of scores, and the standard deviation of the sampling distribution of the mean (also known as the standard error). If the sample is representative of the population, and N > 1, which of the three should be the smallest in value? Why? D. Why do we need to be concerned about the shape of the sampling distribution of the mean when evaluating a null hypothesis using the z test? How is the central limit theorem useful for alleviating this concern?Explanation / Answer
Answer to part A)
The distribution of Raw scores is generally the Z distribution , where each data point represents a specific Z value , corresponding to a data point in the data set
.
Answer to part B)
The distribution of sampling distribution of mean follows normal distribution an deach data point in this distribution represents the mean of each of the samples so formed from the population
.
Answer to part c)
Standard deviation of the sample is equal to standard deviation of the population divided by root of sample size, thus we get to know that the standard deviation of the sample is smallest of all the three values provided in this question
.
Answer to part d)
We are concerned about the shape of the distribution , because only when we know the shape of the distribution can we apply the Z formula or the correct test to the distribution
The central limit theorem is very useful in this situation.
As per the central limit theorem, suppose if a sample is drawn from some unknown distribution , then we can approximate this sample to be drawn from normal distrbution if in case the size of the sample is either 30 or larger. In such a case applying the Z and the T test becomes very easy. all we need is a sample of size 30 or larger in order to apply CLT.
Thus even if the sample is from some unknown population, we can easily apply the normal distribution if the sample is of large size.
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