1-Sample Z-Interval Tests for proportions LESSON (9.2)
To study on how to do this method for my AP Statistics class, I will teach you guys on how to use this method (9.2)
For how I know it, I use this method when I am given a null hypothesis (which is usually the given) and I formulate an alternative hypothesis to try and prove the null hypothesis wrong or right. (reject vs fail to reject) When you reject a null hypothesis (H0) you are basically saying that the null hypothesis is wrong, and that the alternative hypothesis that you formulated matches your data better. When you fail to reject a null hypothesis, you are saying that the data does not give significant evidence to prove that the null hypothesis is wrong. How are we going to test out if the null hypothesis is rejectable or failable to reject?
How I do these types of problems is state, plan, do conclude. It's easy to remember it by making a rectangle and dividing it into four squares so you can evenly divide the problem and get the full credit! State: What parameter, alpha level, null and alternative hypothesis Plan: Method, conditions Do: Perform the calculations (plug in numbers, test statistic, P-value) Conclude: State decision, then write a conclusion based off that decision.
Let's go step by step using the State, Plan, Do, Conclude method.
STATE: (define the parameter, alpha level, null and alternative hypothesis) Basically the parameter is the sample mean or proportion (in this case proportion) of what the problem given us. Population p= the given probability we want to test Alpha level is usually given in the problem, 0.05 and 0.01 is the most common alpha levels. 0.01 is used as an alpha level when we want to be very precise with our calculations. P-hat is usually the actual proportion statistic that one sample gave us (If anyone can look over this and make revisions, I'm not too snazzy on vocab terms yet) Null hypothesis, or Ho, is in the form of population 'p=____'. It always is an equal sign and is the hypothesis that we are testing. Alternative hypothesis, or Ha, is in the form of population 'p>,<,or ≠ ____'. This is the opposite of the null hypothesis. Usually the problem also gives you if you use <,>, or ≠ for the alternative.
PLAN: (identify the method, check conditions) Method for this type of problem is always 1-sample z test for proportions. Formulas you use in the DO part may help to write as well. An important factor on assessing if we can actually accurately calculate is what we call checking conditions. Checking conditions is necessary to understand if the problem will give us a good answer or not. If any of these conditions are not met, you cannot sadly stop the problem (though it will save us time LMAOOO but AP stats teachers will give you an F). You can finish the problem, but on the condition that is not met, write 'Proceed with caution' so the grader knows that you understand that there is not a condition met but still know how to complete the problem. Three conditions WE MUST check! -10% Condition: shows whether or not the sample is independent, and not too large. -Normality: shows whether the problem is normal or not. Must say SRS. -Large Counts: shows if the proportion is large enough to execute the problem.
ok i'm too lazy to type pls tune in my ap stats failures 6-7pm cst tomm!