1.The lifetime of a machine (measured in years, y) follows a normal distribution with variance equal to4y2. A simple random sample of size 100 yields a sample mean equal to 1.3y. Test the null hypothesisthat the population mean is equal to 1.5y, by applying a two-tailed test with 5 percent significancelevel. What is the type I error? Calculate the type II error when the population mean is 2y. Find thegeneral expression of the type II error and then use a computer to plot the power function.
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