Question: The weight of pigs is assumed to follow normal distribution with standard deviation 4 for any farm. We want to do the test whether the means of two pigs farms are same. The sample size for each pig farm is 50. The level of test is 5 %. \({{\bar{x}}_{1}}\) is the sample mean of the first group and is \({{\bar{x}}_{2}}\) the sample mean of the second group.

1. Find the region of \({{\bar{x}}_{1}}-{{\bar{x}}_{2}}\) where we accept the null hypothesis
2. Find the probability of the type II error and the power of the test when the difference of true population means \({{\mu }_{1}}-{{\mu }_{2}}\) is 2.

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