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I am working on an assignment for a course in statistics, and a part of the assignment is to give the null hypothesis of an experiment. The experiment is as followed (short summary):

A company is testing 3 interfaces for a website. They test the interfaces with 15 students, 5 for each interface, and all 5 have a different computer knowledge level. They are all given the same task and the time it takes for each of them to complete the task is the data we're using.

I know need to find the null hypothesis of interest. As far as I understand null hypothesis and the alternative hypothesis should be 2 competing propositions. However, as far as I can tell I have 3 proposition: interface 1 is better, interface 2 is better and interface 3 is better.

What null hypothesis should I have here and why?

Thanks in advance!

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If it is not possible to solve the issue with one set of hypothesis (i.e., one null and one alternative hypotheses) you may need more than one set of hypotheses. – Henrik Jan 12 '12 at 13:21
@Henrik - But the assignment is to find the null hypothesis of interest, and later on we need to decide if we should reject the null hypothesis at a certain significance level, so that suggests that there should be a null hypothesis. – Tiddo Jan 12 '12 at 13:24
One null hypothesis. Your propositions are hypothesis contradicting the null. Which hypothesis is contradicted by each of these propostions? This is your null. And the null is not just the name it tells something about the hypotheses you are looking for. – Henrik Jan 12 '12 at 13:31
Even before getting into the issue of hypothesis testing, how do the skill levels of the $5$ students using Interface $1$ differ from the skill levels of the $5$ students using Interface $2$ and from the skill levels of the $5$ students using Interface $3$? The data gathered might not be very useful in arriving at any defensible conclusions about which Interface is "better" if Interface $3$ required the least time but was also assigned to students who happened to be more skilled than those who used the other Interfaces. – Dilip Sarwate Jan 12 '12 at 14:09
The reasonable approach is to use ranking and selection instead of testing. – Xi'an Jan 12 '12 at 19:53

1 Answer

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This information should be in your textbook and/or course notes. There are more than 1 testing procedure that creates a single overall hypothesis to test (then you can use follow-up or post hoc procedures to look at additional comparisons of interest). Two commonly used (and taught in early stats classes) methods are Analysis of Variance (ANOVA or AOV) and $\chi^2$ tests on two-way tables (sometimes called contingency tables). One of those may be what the question is expecting you to use, look the details up in your textbook (or wikipedia, or some other source) and see what hypotheses are used in the examples.

Hint: you say there are 3 hypotheses about which is best, but does one of them have to be the best?

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