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Apr 3, 2024

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Stat 20 Wrong by Design Question 1 For each of the following sets of hypotheses, determine whether committing a Type I error or a Type II error has greater real-world consequences. Explain your decision. Part A Imagine that the San Francisco Giants hold a book donation promotion for one of their games where every individual who brings a used book to the stadium is allowed free entry. 𝐻 0 : The number of individuals who wish attend the game will be no more than the capacity of the stadium. 𝐻 𝐴 : The number of individuals who wish to attend the game will exceed the capacity of the stadium. Part B 𝐻 0 : A new operating system is no more effective for Carbon Health to use on the computers at its clinics than the old operating system. 𝐻 𝐴 : A new operating system is more effective for Carbon Health to use on the computers at its clinics than the old operating system. Part C 𝐻 0 : The rate of COVID-19 infection on campus has not changed since last month. 𝐻 𝐴 : The rate of COVID-19 infection on campus has increased since last month.

Question 2 A food safety inspector is called upon to investigate a restaurant with a few customer reports of poor sanitation practices. The food safety inspector uses a hypothesis testing framework to evaluate whether regulations are not being met. If he decides the restaurant is in gross violation, its license to serve food will be revoked. Part A Write the hypotheses in words. Part B What is a Type 1 Error in this context? Part C What is a Type 2 Error in this context? Part D Which error is more problematic for the restaurant owner? Why? Part E Which error is more problematic for the diners? Why? Part F As a diner, would you prefer that the food safety inspector requires strong evidence or very strong evidence of health concerns before revoking a restaurant’s license? Explain your reasoning.

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