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7.1 Notes (continued) AP Statistics Types of Errors Regardless of which hypothesis is the claim, always start by assuming that H0 is true. One of two decisions is made: Decision made on incomplete data! (Sample rather than population) What if we make a mistake???? Type I Error: Type II Error: Decision Actual Truth of H0 H0 is true H0 is false Do not reject H0 Reject H0 Example: The USDA limit for salmonella contamination for chicken is 20%. A meat-packing company claims that its chicken falls within the limit. You perform a hypothesis test to determine whether the company’s claim is true. When will a type I or type II error occur? What are the outcomes? _________________________: maximum allowable probability of making a type I error. It is denoted by ∝ (lowercase Greek letter alpha) Small level of significance probability of rejecting a true H0 small Test Statistic: statistic compared to parameter in H0 Decisions, Decisions, Decisions…. One way to decide whether to reject H0 is to decide if the probability value, P-value, is less than or equal to the significance level: 𝑃 ≤∝ 𝑃 >∝ BUT… we need to talk about tails first! Example: For each claim, state H0 and Ha. Then determine whether the hypothesis test is a lefttailed test, right-tailed test, or two-tailed test. Sketch a normal sampling distribution and shad the area for the P-value. ~A university claims that the proportion of its students who graduate in four years is 82% ~A water faucet manufacturer claims that the mean flow rate of a certain type of faucet is less than 2.5 gallons per minute. ~A cereal company claims that the mean weight of the contents of its 20-ounce size cereal boxes is more than 20 ounces. Example: You perform a hypothesis test for each of the following claims. How should you interpret your decision if you reject H0? If you fail to reject H0? ~H0 (Claim): A university claims that the proportion of its students who graduate in four years is 82%. ~H0 (Claim): A government safety administration claims that the mean stopping distance (on a dry surface) for a Chevrolet Malibu is less than 148 feet. Assignment: Page 331 # 17 – 33 odd