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What does the researcher hope to do with the null hypothesis (the opposite of the research hypothesis)?
Be able to reject the null hypothesis and accept the research hypothesis
When you accept the Null Hypothesis you are certain that the Null Hypothesis is correct?
No, you are never certain.
How do you know if you have enough information to draw an hypothesis test in statistics?
You can test a hypothesis with very little information. For hypothesis testing you will have a null hypothesis, and alternative and some test statistic. The hypothesis test consists of checking whether or not the test statistic lies in the critical region. If it does, then you reject the null hypothesis and accept the alternative. The default option is to stick with the null hypothesis.If the number of observations is very small then the critical region is so small that you have virtually no chance of rejecting the null: you will default to accepting it.Different test have different powers and these depend on the underlying distribution of the variable being tested as well as the sample size.
If Relationship between statistical significance and rejectingaccepting an hypothesis?
I believe you asked for the relationship between "statistical significance" and hypothesis testing. In hypothesis testing, we state the null and alternative hypothesis, then in the traditional method, we use a test statistic and a significance level, alpha, to decide whether to accept or reject the null hypothesis in favor of the alternative. If our test statistic falls in the reject area (critical region) of the sampling distribution, then we reject the null hypothesis. If not, we accept it. There is the second method, the p-value method, which is similar in that an alpha value has to be selected. Now, the term "statistical significant result", as used in statistics, means a result (mean value, proportion or variance) from a random sample was not likely to be produced by chance. When we reject the null hypothesis in favor of the alternative, we indicate our data supports an alternative hypothesis, so our result is "statistically significant." Let me use an example. Generally workers arrive at work a few minutes more or less than required. Our null hypothesis will be an average lateness of 5 minutes, and our alternative hypothesis will be greater than 5 minutes. Our data shows an average lateness of 12 minutes, and our test statistic, taking into account the variance and sample size, and our chosen alpha level, concludes that we reject the null hypothesis, so the 12 minute average is a significantly significant result because it supported rejection of the hypothesis. The problem is that significant, in common usage, means important or meaningful, not trivial or spurious. The sample used to calculate late time may have been not randomly chosen, more people come to work late in bad weather. The sample is to make inferences on the a general population, but there is no static population in this case, as a company hires and fires employees. So, since our data is flawed, so can our conclusions. Used as a technical term in statistics, statistical significance has a much more rigorous and restricted meaning, which can lead to confusion. See: http://en.wikipedia.org/wiki/Statistical_significance
Fail to reject the null hypothesis rather than Accept the null hypothesis?
This is the way experimenters and statisticians phrase it, but it's more than a word choice distinction. The null hypothesis is a negative and can not, by definition, be proved. To test the hypothesis, "A cat runs through my yard at night," we could set up various cat catchers, movement measuring devices, measure the amount of cat food in various locations on the lawn. If we don't find any evidence, we can say, "There's no proof that a cat ran through my yard for however long the experiment lasted." What we do is accept the null hypothesis, "No cat runs through my yard at night." We don't have proof that one didn't because you can't get proof of a negative, but, in the absence of proof that one did, we do not reject the null hypothesis of "No cat."
