Question: Recall that Type II or beta error is the probability of failing to reject the null hypothesis when it is in fact false. Assume that you are testing the hypothesis that μ = μ0 against the alternative that μ ≠ μ0 at a level of significance α0. If the population variance σ2 is known, obtain an expression for the beta error & then use this expression to calculate the level of beta error in the following situation. You are testing the null hypothesis that the population mean is equal to ten, against the alternative that the population mean is not equal to ten. The actual population mean is twelve. You know the population standard deviation is 3, the sample mean is 10.50, the sample size is fifteen, the data is normally distributed & the level of significance of the test is 0.05. [Clue: You will fail to reject the null hypothesis if your test statistic falls in the “do-not-reject region”, so calculate the probability that it will fall within this region if the true mean differs from the hypothesized mean.]