AP Statistics : Significance
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Example Questions
Example Question #6 : How To Establish A Null Hypothesis
For his school science project, Timmy wants to determine whether the ants in his neighborhood have colonies that are sized differently than normal. His research shows that the average Harvester colony has around 4000 ants. He counts the number of ants in 5 colonies and determines that the average colony size is 3,700 ants. What is the appropriate null hypothesis for his science project?
Timmy does not have a directional hypothesis, he only wants to know whether local ant colonies are different from average. Therefore he thinks the colonies could be bigger or smaller than average. This means his alternative hypothesis is that the ant colonies are NOT equal to the average colony size of 4000 ants. His null hypothesis must include all other outcomes, which in this case is that local ant colonies are equal to the average size of 4000 ants.
Example Question #21 : Significance Logic And Establishing Hypotheses
A study would like to determine whether meditation helps students improve focus time. They used a control group of 30 students and compared their focus time to a group of 30 meditating students and compared their average time spent meditating. What is the appropriate null hypothesis for this study?
Because we are comparing two samples, the hypothesis takes the form of Mu1- Mu2. Because we are testing the claim that meditation increases average study time, the null hypothesis must cover all other outcomes. That means the null hypothesis is that the difference between control minus meditation is greater than or equal to zero.
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