Question: Assume a population has the following elements: {2; 5; 8; 12; 13}. Samples of size 3 are drawn without replacement. 1.1) Find the sampling distribution

Assume a population has the following elements: {2; 5; 8; 12; 13}. Samples of size 3 are drawn without replacement.

1.1) Find the sampling distribution of the sample mean.

1.2) Use (1.1) to find the mean and variance of the sample mean.

1.3) Find an unbiased estimate of the population variance.

1.4) Use the normal approximation and (1.2) to construct a 95% confidence interval for the population mean.

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