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Two statistics questions

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Question 1:

When a researcher has two samples with two means, one of the assumptions for two samples is independence of between the two samples. What does this mean? What happens if the independence assumption is violated?

Questions 2:

What are the differences among a proportion, a percentage, and a ratio? When would a researcher use a hypothesis test for the difference in two population proportions? Explain.

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Question 1:

When a researcher has two samples with two means, one of the assumptions for two samples is independence of between the two samples. What does this mean? What happens if the independence assumption is violated?

ANSWER:

Independence of the two samples means that the choosing of the first sample did not influence the choosing of the other sample, and vice versa.

For example, if you were comparing running speed in two different brands of running shoes, you could look at two samples of people running a 100 m dash -- one sample of people running in Brand A and one sample of people running in Brand B. If those two groups were picked independently of one another, these samples would be independent. If, instead, you had the same group of people run the race twice (once in each brand of shoe), these samples ...

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