Subjects statistics

Type I Ii Errors 5Fbcc3

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1. **Stating the problem:** We are given hypotheses about the level of home ownership and asked to identify what Type I and Type II errors would be in this context. 2. **Hypotheses:** - Null hypothesis ($H_0$): The level of home ownership remains the same. - Alternative hypothesis ($H_a$): The level of home ownership changes (or rises). 3. **Type I error definition:** A Type I error occurs when we reject the null hypothesis when it is actually true. 4. **Type II error definition:** A Type II error occurs when we fail to reject the null hypothesis when the alternative hypothesis is actually true. 5. **Applying to the problem:** - Type I error: Concluding that home ownership is on the rise (rejecting $H_0$) when in fact the tax breaks don't help (null is true). - Type II error: Failing to conclude that home ownership is on the rise (not rejecting $H_0$) when in fact the tax breaks do help (alternative is true). 6. **Answer choices:** - Type I error: "The city concludes that home ownership is on the rise, but in fact the tax breaks don't help." - Type II error: "The city abandons the tax breaks, but they were helping." **Final answers:** - Type I error: The city concludes that home ownership is on the rise, but in fact the tax breaks don't help. - Type II error: The city abandons the tax breaks, but they were helping.