assume that a population consist of 5 students and the marks obtained by them in a certain statistics class are 21,14,15,17 and18. draw all possible random samples of two students when simple random sampling is performed with replacement. calculate the mean and standard deviation for each sample and compare it with the popoulation mean and standard deviation.
Answers
Step-by-step explanation:
In Note 6.5 "Example 1" in Section 6.1 "The Mean and Standard Deviation of the Sample Mean" we constructed the probability distribution of the sample mean for samples of size two drawn from the population of four rowers. The probability distribution is:
x−−P(x−−)152116154216156316158416160316162216164116
Figure 6.1 "Distribution of a Population and a Sample Mean" shows a side-by-side comparison of a histogram for the original population and a histogram for this distribution. Whereas the distribution of the population is uniform, the sampling distribution of the mean has a shape approaching the shape of the familiar bell curve. This phenomenon of the sampling distribution of the mean taking on a bell shape even though the population distribution is not bell-shaped happens in general. Here is a somewhat more realistic example.
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