1. A 10 Step Quest Every Time!

2. Overview When we hypothesis test, we are trying to investigate whether or not a sample provides strong evidence of something. We start off by assuming the something is not true. Then we see how reasonable our sample is. If the sample is crazy unlikely, that means that our assumption that the something being untrue is also crazy unlikely. So it is far more likely that the something is therefore true. If the sample is likely enough, that means that we pretty much learned nothing either way from our sample.

3. Step 1 – Test Selection When we do a hypothesis test, we have to determine which test to use. When we only have 1 sample, we use a 1 sample test. When we are comparing two samples to each other, we use a 2 sample test. When we have proportional data, we use a proportion test. When we have quantitative data, we use a t test (unless we magically know sigma). For a 2 sample t test, we also need to determine if it is independent or paired.

4. Step 1 – Test Selection This leads to the following tests: 1 proportion z 2 proportion z 1 sample z (when we magically know sigma) 1 sample t 2 sample independent t 2 sample paired t Each one of these tests corresponds with a confidence interval, meaning there are 6 of those as well.

5. Step 1 – Test Selection So far we only know the 1 proportion z test, so on Chapter 20’s quiz, you should totally use that one.

6. Step 2 – Check Conditions The type of test we end up doing will have 3 to 5 conditions for us to check. For the 1 proportion z test, there are 4 conditions. They are Random, Independent, Less than 10%, and Success/Failure.

7. Step 2 – Check Conditions For Random, we usually will just say that the problem says it was random. Otherwise, we either need to give a sensible reason to presume it is random (like self-respecting scientists should use randomization) or give a sensible reason to presume it is not random.

8. Step 2 – Check Conditions For independent, you typically just point out that one outcome does not affect a separate outcome. For Less Than 10%, you multiply the sample size by 10, and then state that the population has more than that amount of whatevers.

9. Step 2 – Check Conditions For Success/Failure, you need to know how many subjects were in each category (safe v.s unsafe, support vs. do not support, etc.) and be sure that each group is over 10. To do this, you must multiply the sample size by the p you will use in your H 0 and the complement of the p you will use in your H 0. This might mean you have to determine your H 0 before you can actually do this.

10. Step 3 – Write The Hypotheses You should start by determining the alternative hypothesis first. The wording of the actual question is meant to provide the necessary clues on how the alternative should be written. Writing the alternative requires making three distinct decisions. You need to determine which variable, inequality sign, and number to use.

11. Step 3 – Write The Hypotheses If the data is proportional, the variable is p. If the data is quantitative (which is next unit), the variable is μ. The wording of the question helps us determine the inequality sign. If they are asking about finding evidence of a “change” or a “difference” then you use ≠. If they are asking about finding evidence of an “increase” or some other such word, then you use >. A word like “decrease” is a key word for <.

12. Step 3 – Write The Hypotheses Because on a ≠ test we are interested in a change in a positive or a negative direction (increases and decreases are both changes), it is referred to as a 2- tailed test. This is because we are interested in both tails of the normal curve. If you are not convinced you should be using a alternative, the ≠ is the default.

13. Step 3 – Write The Hypotheses For a < test, we are only focused on a decrease. We refer to this as a left-tailed or lower-tailed test. For a > test, we are only focused on an increase. We refer to this as a right-tailed or upper-tailed test.

14. Step 3 – Write The Hypotheses The number in your alternative hypotheses is not the number generated by your sample. It will be a different number, and will usually be based on either previous data or else the known value for a similar group. Occasionally, you will need to determine the number using critical thinking. The most common examples are that fair coins and simple majorities.

15. Step 4 – Write The Formula The reason you should write the formula is that it is evidence of doing some work. This can score you partial credit on the quiz, test, and even on the final. The most intense version of the formula is:

16. Step 5 – The Calculating, Part 1 The p comes from H 0, the p-hat comes from the sample, and the n is the size of the sample. Do not forget to store values in the calculator instead of rounding off. The formula gives you a z-score, but remember you will need that z-score to get a p-value.

17. Step 5 – The Picture On your picture, you should label the center with p, and mark the p-hat, shading towards the tail of the graph. If it is a ≠ test, shade both sides of the graph. You do not need to label the other side.

18. Step 6 – The Calculating, Part 2 Since we only want the probability from the tail, we use normalcdf in the following way. If z is positive: normalcdf(z,5) If z is negative: normalcdf(-5,z) If it is a ≠ test, we double the value we get, since we need the area for both tails of the graph.

19. Step 7 – Determine Alpha It is.05 unless the problem says otherwise. Here are some examples of how that would happen: Perform a hypothesis test. (α =.01) Perform a hypothesis test at the 10% significance level. Perform a hypothesis test using a.005 significance level. Perform a hypothesis test using 2% significance.

20. Step 8 – Write The Decision Rules If p-value <.05, reject H 0. If p-value ≥.05, DNR H 0. If you have a different alpha, write that instead of.05 in the above rules.

21. Step 9 – Make Your Decision Low p-value: “Since p-value = _____ <.05, reject H 0.” High p-value: “Since p-value = _____ >.05, DNR H 0.”

22. Step 10 – Write Your Conclusion Rejecting is evidence!!!!! Reject H 0 : “There was sufficient evidence that blahblahblah.” DNR H 0 : “There was not sufficient evidence that blahblahblah.” The blahblahblah involves regurgitating the problem wording.