Assignment 24

We already went through a bulk of assignment 24, but I realize it was very rushed, so I want to go through an example that isn't on your homework (but will clearly help you do all of your homework.) It also may be a good idea to go through this example as an exam review if you have already finished the homework. Just try to answer the questions before looking at my answers.

Problem (in honor of this Thursday nights event):

The Capitol wants to know what the average survival time in hours of the tributes from each of the twelve districts will be for the 74th hunger games. Sample data was collected from a random sample of 20 hunger games. Data can be considered to be normally distributed.

1. What type of study is this?

Observational. The hunger games (the past 20 sampled) have already happened. We are observing. (Although the hunger games themselves are certainly not an observational study...)

2. What are the hypothesis of this test?

Ho: µ1=µ2=µ3=µ4=µ5=µ6=µ7=µ8=µ9=µ10=µ11=µ12

Ha: Not all means are the same.

Below is the ANOVA output.

3. Is the normality condition met?

Yes, stated in the problem.

4. Is the randomization condition met?

Yes, stated in the problem. (could be met through graphing as well).

5. Is the equal variance condition met?

The largest Standard Deviation is: 28. The Smallest standard deviation is: 20

28/20=1.4 < 2. This condition is met.

6. How does p-value compare to alpha?

We can find the p-value on the chart. It is 0. Because we have 95% confidence intervals, that gives us an alpha=0.05. Thus, 0<0.05, so we are significant. Thus, one of the means does differ.

7. What does this mean in context? (In other words, what do the confidence intervals tell us? or What means differ? or Are some districts likely to last longer? All of these ways are reasonable ways to ask the same question).

We can see that districts 3-11 have confidence intervals that significantly overlap. This shows that their true means are unlikely to differ by much. However, we can see that districts one and two's confidence intervals are much larger, showing that on average they last much longer. District 12's confidence interval shows us that it differs by them lasting much less time in the arena.

May the odds ever be in your favor...(can you tell I'm excited?)

-Hillary