Which type of error would the team owner prefer to

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Which type of error would the team owner prefer to have a small probability, assuming his/her priority is not to have to pay a larger salary if the player has not really improved? Explain. Player: Manager: Practice Problem 1.6A For the research study on the mortality rate at St. George’s hospital (Investigation 1.3), the goal was to compare the mortality rate of that hospital to the national benchmark of 0.15. Suppose you plan to monitor the next 20 operations, using a level of significance of 0.05. Also suppose the actual death rate at this hospital equals 0.25. (a ) If you were to conclude that the hospital’s death rate exceeds the natio nal benchmark when it really does not, what type of error would you be committing ( Choose one : Type I, Type II, Both, Neither)? (b) If you were to conclude that the hospital's death rate does not exceed the national benchmark when it really does, which type of error would you be committing( Choose one : Type I, Type II, Both, Neither)? (c) Which error, Type I or Type II, would you consider more critical here? Explain. (d) Use the Power Simulation applet to determine the rejection region for a sample of 20 patients. (e) What is the approximate power for this rejection region? Write a one-sentence interpretation of what w e mean by “power” here.
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Chance/Rossman, 2015 ISCAM III Investigation 1.6 58 Factors that Influence Power You have learned through this investigation that there are two types of errors that one can make with tests of significance. So far in Investigation 1.6, you found the manager might become convinced that the player has improved when he really has not (a Type I error), or the manager might not be convinced that the player has improved when he really has (a Type II error). Now you will explore how we might reduce these error probabilities. (m) Suppose the manager wants to reduce the probability of a Type I error. Should he instead require the player to make at least 8 hits or at least 10 hits? 8 10 Explain. (n) In the Power Simulation applet, make the change suggested in (m) by choosing Rejection Region from the pull-down menu and specifying your choice for the cut-off value for the number of hits. Press Count and report the new empirical level of significance (estimated probability of a type I error). Did the estimated probability of a Type I error increase or decrease? (o) Also note the new approximate power with this smaller probability of a Type I error. Does power increase or decrease? What does this say about the probability of a Type II error? Discussion: The probabilities of a Type I error and a Type II error have an inverse relationship. If we change the level of significance to decrease the probability of a Type I error, we will increase the probability of a Type II error. Power and Type II error on the other hand are directly and inversely related, as power is one minus the probability of Type II error. In some studies, you may seek a balance between these Type I and Type II errors. More typically, especially if a Type I error is considered more
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