Question: Independent random samples of 64 observations each are chosen from two normal populations with the following means and standard deviations:

Let \(\bar{x}_{1}\) and \(\bar{x}_{2}\) denote the two sample means.

1. Give the mean and standard deviation of the sampling distribution of \(\bar{x}_{1}\).
2. Give the mean and standard deviation of the sampling distribution of \(\bar{x}_{2}\).
3. Suppose you were to calculate the difference \(\left(\bar{x}_{1}-\bar{x}_{2}\right)\) between the sample means. Find the mean and standard deviation of the sampling distribution of \(\left(\bar{x}_{1}-\bar{x}_{2}\right)\).
4. Will the statistic \(\left(\bar{x}_{1}-\bar{x}_{2}\right)\) be normally distributed? Explain.

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