Download 7.1 Notes (continued) AP Statistics Types of Errors Regardless of

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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