2.4.5 Practice Computing Probilities for Type 1 & Type 2 Errors _2004005_6b24P2ejn.pdf

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1. For each of the following, state the null and alternative hypotheses, the type 1 and type 2 errors associated with the hypotheses, and the consequences of each error. A. The decision to implement changes in the current math program at a junior high in Bigcity will be based on the sample of the students scores on a standardized math exam. If the average is less than the statewide average of 89, all math teachers will have to participate in a workshop to revise the curriculum. Ho: u = 89 (The mean score on the standardized math exam is 89) Ha: u < 89 (The mean score on the standardized math exam is less than 89) Type 1 error: they conclude the standardized math score is not 89 when it actually is. This could have the school implement changes even though they would not need to. Type 2 error: They conclude the standardized math score is 89 when it is actually not. This could hurt the kids at the school because they would not want to implement changes when they actually need to. B. Expensive Clothing, Inc. thinks it’s a good year and wants to reward its customers. In a typical year, sales are $75 per customer. If a random sample of this year’s sales indicate a better than average year (average sales per customer are higher than 75), a $10 coupon will be given out for two weeks to each customer who spends at least $75. Ho: u = 75 dollars (The mean amount of sales per customer is 75 dollars in a year) Ha: u > 75 dollars (The mean amount of sales per customer is greater than 75 dollars in a year) Type 1 error: The store concludes they are not having a better than average year, when it actually is. This would hurt the customers because they are spending more money at the store.

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