The Grants have been able to provide clear evidence for natural selection and supported Darwin's theory. The hypothesis was that natural selection can occur many times in a lifetime.
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A hypothesis is the first step in running a statistical test (t-test, chi-square test, etc.) A NULL HYPOTHESIS is the probability that what you are testing does NOT occur. An ALTERNATIVE HYPOTHESIS is the probability that what you are testing DOES occur.
Failing to reject a false null hypothesis.
I think you are asking: What is hypothesis testing in the field of statistics. See: http://en.wikipedia.org/wiki/Statistical_hypothesis_testing
No. The null hypothesis is assumed to be correct unless there is sufficient evidence from the sample and the given criteria (significance level) to reject it.
A non-directional research hypothesis is a kind of hypothesis that is used in testing statistical significance. It states that there is no difference between variables.