AP Statistics Chapter 9

STUDY
PLAY
Significance Test
A formal procedure for using observed data to decide between two competing claimes
Null Hypothesis
Claim we weigh evidence against in a significance test
Alternative Hypthesis
The claim that we are trying to find evidence for in a significance test
One-Sided
It states that a parameter is larger than the null hypothesis value or states that the parameter is smaller than the null value
Two-Sided
It states that the parameter is different from the null hypothesis value (it could be either larger or smaller)
P-Values
The probability, computed assuming the null hypothesis is true, that the statistic would take a value as extreme as or more extreme than the one actually observed, in the direction specified by the alternative hypothesis
Reject the Null Hypothesis
If the observed result is too unlikely to occur just by chance when the null hypothesis is true, we can ____________________________________________ and say that there is convincing evidence for the alternative hypothesis
Fail to Reject Null Hypothesis
If the observed result is not very unlikely to occur when the null hypothesis is true, we should _______________________________________________ and say that we do not have convincing evidence for the alternative hypothesis
Statistically Significant at the Level (alpha)
If the p-value is smaller than alpha, we say that the results of a study are _____________________________________
Type I Error
If we reject the null hypothesis when the null hypothesis is true
Alpha
P(Type 1 Error)
Type II Error
If we fail to reject the null hypothesis when the alternative hypothesis is true
Beta
P(Type 2 Error)
Test Statistic
Measures how far a sample statistic diverges from what we would expect if the null hypothesis were true, in standardized units.
Z-Score for the Statistic
The "test statistic" is the same thing as the ____________________________
Significance Test - four step process
STATE: what hypotheses do you want to test, and at what significance level?
PLAN: Name test. Check conditions.
DO: if the conditions are met, perform calculations
-compute the test statistic
-find the p-value
CONCLUDE: make a decision about the hypotheses in the context of the problem
Conditions for a One-Sample Z-Test and One-Sample T-Test
Random, Normal, Independent
One-sample z test for a proportion
Use this test to test a claim regarding a single proportion

If the conditions are met. To test the hypothesis null hypothesis:P=Po, compute the z statistic (see image for formula)
Find the p-value by calculating the probability of getting a z statistic this large or larger in the direction specified by the alternative hypothesis Ha:
Ha:p>p0
Ha:p<p0
Ha:p cannot equal p0
Power
The _________________ of a test against a specific alternative is the probability that the test will reject the null hypothesis at a chosen significance level alpha when the specified alternative value of the parameter is true. We made the correct decision.
Formula for the Power of the Test
1 - beta
One-sample t test
Use this test to test a claim regarding a single mean (WHEN THE STANDARD DEVIATION OF THE POP IS UNKNOWN)
Paired Data
Study designs that involve making two observations on the same individual or one observation on each of two VERY similar individuals result in ...
Paired t procedures
When paired data result from measuring the same quantitative variable twice, we can make comparisons by analyzing the differences in each pair. If the conditions for inference are met, we can use one-sample t procedures to perform inference about the mean difference mean(d). These methods are called __________________________________