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is used to increase the level of confidence, which in turn reduces Type I errors. The chances of making a Type I error are reduced by increasing the level of confidence that the event A and measurement B are within our control and are not being caused by chance or some other external events. This results in more stringent criteria for rejecting the null hypothesis (such as specific pass/fail criteria), – (failing to reject H0 when it was really false and should have been rejected)!

You won’t be required to actually perform a real experiment or survey in elementary statistics (or even disprove a fact like “Pluto is a planet”!), so you’ll be given word problems from real-life situations. You’ll need to figure out what your hypothesis is from the problem. This can be a little trickier than just figuring out what the accepted fact is. With word problems, you are looking to find a fact that is nullifiable (i.e. something you can reject).

For example, we accept the alternative hypothesis H and reject the null H, if an event is observed which is at least a-times greater under H than under H.

The test for homogeneity, on the other hand, is designed to test the null hypothesis that two or more , according to some criterion of classification applied to the samples.

The larger the p-value is when compared with (in one-sided alternative hypothesis, and /2 for the two sided alternative hypotheses), the less evidence we have for rejecting the null hypothesis.

For this goodness-of-fit test, we formulate the null and alternative hypothesis as H_{0}: f_{Y}(y) = f_{o}(y)

H_{a}: f_{Y}(y) f_{o}(y) At the level of significance, H_{0} will be rejected in favor of H_{a} if C is greater than .

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For the goodness-of-fit sample test, we formulate the null and alternative hypothesis as H : f_{Y}(y) = f_{o}(y)

H : f_{Y}(y) f_{o}(y) At the level of significance, H will be rejected in favor of H if is greater than However, it is possible that in a goodness-of-fit test, one or more of the parameters of f_{o}(y) are unknown.

Therefore, there is not sufficient evidence to reject the null hypothesis that the two correlation coefficients are equalClearly, this test can be modified and applied for test of hypothesis regarding population correlation based on observed r obtained from a random sample of size n:provided | r | 1, and | | 1, and n is greater than 3.

The p-value, which directly depends on a given sample attempts to provide a measure of the strength of the results of a test for the null hypothesis, in contrast to a simple reject or do not reject in the classical approach to the test of hypotheses.

Now, using the known distribution of the test statistic, we construct ranges of values for which we reject (rejection region) and fail to reject (acceptance region) the null hypothesis.

If we are looking for differences, we reject the null hypothesis that the groups are the same for the respective alternative if * t *> * T*_{df,alpha,} * t *< - * T*_{df,alpha, }or |* t*| > * T*_{df, alpha/2}, where alpha is the prespecified type I error for the decision to be made.

If there is minimal information, it will be difficult to statistically reject the null hypothesis; hence, sample size calculations are done in order to ensure that there is sufficient information from which to make a decision.

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