Question

What is a null hypothesis and what is an alternative hypothesis?  How do you choose the null hypothesis in general? Give an example What is type I error? What is type II error? What is the significance level? What is the power of the test? What is the p-value of a hypothesis test?.

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Answer 1

Null hypothesis and Alternative hypothesis
(1) In null hypothesis, no statistical significance exists in a set of given observations.
(2) In null hypothesis, no variation exists between variables or that a single variable is no different than its mean.
(3) The opposite of the null hypothesis is known as the alternative hypothesis.
(4) In hypothesis testing, a proposition that is accepted if the null hypothesis is rejected.
(5) The alternative hypothesis is the hypothesis used in hypothesis testing that is contrary to the null hypothesis.
(6) It is usually taken to be that the observations are the result of a real effect (with some amount of chance variation superposed).
(7) The null hypothesis is the initial statistical claim that the population mean is equivalent to the claimed.
Example: Assume the average time to wash a cloth in washing machine is 36 minutes. Therefore, the null hypothesis would be stated as, "The population mean is equal to 36 minutes." Conversely, the alternative hypothesis is the hypothesis that is accepted if the null hypothesis is rejected.
How to choose Null hypothesis
(1) The null hypothesis is nearly always "something didn't happen" or "there is no effect" or "there is no relationship" or something similar.
(2) Figure out the hypothesis from the problem.
(3) The hypothesis is always hidden in a word problem.
(4) Sometimes a statement of what we expect to happen in the experiment.
(5) If the hypothesis doesn’t come true. If the recovery time isn’t greater, then there are only two possibilities, that the recovery time is equal to or less than.
Type I error:
(1) A type I error is the rejection of a true null hypothesis ("false positive" finding)
(2) A type II error is failing to reject a false null hypothesis ("false negative" finding).
p value of a hypothesis test
(1) The significance level, also denoted as alpha or ?, is the probability of rejecting the null hypothesis when it is true. For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.
(2) A p value is used in hypothesis testing to help us support or reject the null hypothesis. The p value is the evidence against a null hypothesis.

(3) P values are expressed as decimals although it may be easier to understand what they are if you convert them to a percentage. For example, a p value of 0.0254 is 2.54%. This means there is a 2.54% chance our results could be random (i.e. happened by chance). That’s pretty tiny. On the other hand, a large p-value of .9(90%) means your results have a 90% probability of being completely random and not due to anything in your experiment. Therefore, the smaller the p-value, the more important.