H.2. The manager of a company knows that the volume of the sales of its workers can be modeled by a normal distribution with an expected value of 580 monetary units and a standard deviation equal to 80. For various reasons, the manager believes that "there has been an increase in the sales, so that its average amount has moved to 600 monetary units, while maintaining the standard deviation and normality of the population. To analyze the validity of this belief, the director of the company selects a sample of 100 sellers. la. What is the significance level of the test if the decision rule is to reject the null hypothesis HO:u=580 with respect to the H1: u=600 when the value is higher than 590 monetary units? 1b. Which is the power of the test? 1c. Graph the two errors. 1d. In order to reduce the level of significance, the decision criterion is established as follows: "HO is rejected if the average sample is larger than 595". Determine the new significance level and the power of the test. Graph them. 1e. Check how the significance level and the power of the test vary, if the size of the sample is set to 144 elements