Which hypothesis is it?

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Topic: Exact tests for tables · more questions on this topic

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1. Eighty patients are randomised, 40 to each of two drugs, and each is recorded as improved or not. (b) One hundred visitors to a clinic are asked two questions, whether they exercise weekly and whether they have high blood pressure. (c) Three factories each test 30 items and count the defectives.

For each study, say whether the natural null hypothesis is homogeneity or independence, and which margins are fixed by the design.

Worked answer

1. Homogeneity. The drug assignment fixes the two row totals at 40. The null is that the chance of improvement is the same under both drugs. (b) Independence. One sample is classified by two questions, and both margins are random. The null is that exercise and blood pressure multiply in the joint distribution. (c) Homogeneity. Each factory’s sample size is fixed. The null is that the defective probability is the same in all three factories.