Significance Tests / Hypothesis Testing
The null hypothesis reflects that there will be no observed effect for our experiment.
Support or Reject Null Hypothesis
Sample question: A researcher claims that more than 23% of community members go to church regularly. In a recent survey, 126 out of 420 people stated they went to church regularly. Is there enough evidence at α = 0.05 to support this claim? Use the PValue method to support or reject null hypothesis.
Sample question: A researcher claims that Democrats will win the next election. 4300 voters were polled; 2200 said they would vote Democrat. Decide if you should support or reject null hypothesis. Is there enough evidence at α=0.05 to support this claim?
Hypothesis testing is vital to test patient outcomes.
NOTATION: The notation H_{o} represents a null hypothesis and H_{a} represents an alternative hypothesis and p_{o} is read as pnot or pzero and represents the null hypothesized value. Shortly, we will substitute μ_{o} for when discussing a test of means.
Usually, the null hypothesis is boring and the alternative hypothesis is interesting. For example, let's say you feed chocolate to a bunch of chickens, then look at the sex ratio in their offspring. If you get more females than males, it would be a tremendously exciting discovery: it would be a fundamental discovery about the mechanism of sex determination, female chickens are more valuable than male chickens in egglaying breeds, and you'd be able to publish your result in Science or Nature. Lots of people have spent a lot of time and money trying to change the sex ratio in chickens, and if you're successful, you'll be rich and famous. But if the chocolate doesn't change the sex ratio, it would be an extremely boring result, and you'd have a hard time getting it published in the Eastern Delaware Journal of Chickenology. It's therefore tempting to look for patterns in your data that support the exciting alternative hypothesis. For example, you might look at 48 offspring of chocolatefed chickens and see 31 females and only 17 males. This looks promising, but before you get all happy and start buying formal wear for the Nobel Prize ceremony, you need to ask "What's the probability of getting a deviation from the null expectation that large, just by chance, if the boring null hypothesis is really true?" Only when that probability is low can you reject the null hypothesis. The goal of statistical hypothesis testing is to estimate the probability of getting your observed results under the null hypothesis.
That’s How to State the Null Hypothesis!
In a mathematical formulation of the null hypothesis there will typically be an equal sign. This hypothesis is denoted by H_{0}.
The null hypothesis is what we attempt to find evidence against in our hypothesis test. We hope to obtain a small enough that it is lower than our level of significance and we are justified in rejecting the null hypothesis. If our pvalue is greater than alpha, then we the null hypothesis.
Null and Alternative Hypotheses for a Mean

Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72
Five Steps in a Hypothesis Test (Note: some texts will label these steps differently, but the premise is the same)

Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72
Why the Null Hypothesis (H)?

What does it mean to have a null hypothesis accepted?
The null hypothesis for the independent ttest is that the population means from the two unrelated groups are equal:
Failing to reject a hypothesis means a ..
Now, I want to design a test where my hypothesis is that a function of two samples is the same (which is the opposite of traditional statistics tests where the hypothesis is that the two samples are different). So, my null hypothesis becomes that the two samples are different. How should I design such a test? Will it be as simple as saying that if the pvalue is lesser than 5% we can accept the hypothesis that there is no significant difference?
failing to reject the null hypothesis does not mean ..
If the null hypothesis is not rejected, then we must be careful to say what this means. The thinking on this is similar to a legal verdict. Just because a person has been declared "not guilty", it does not mean that he is innocent. In the same way, just because we failed to reject a null hypothesis it does not mean that the statement is true.
Learn About Null Hypothesis and Alternative Hypothesis
Traditionally, the is a point value. (It is typically $0$, but can in fact be any point value.) The alternative hypothesis is that the true value is any value other than the null value. Because a continuous variable (such as a mean difference) can take on a value which is indefinitely close to the null value but still not quite equal and thus make the null hypothesis false, a traditional point null hypothesis cannot be proven.
to reject a null hypothesis it does not mean ..
The null hypothesis for an experiment to investigate this is “The mean adult body temperature for healthy individuals is 98.6 degrees Fahrenheit.” If we fail to reject the null hypothesis, then our working hypothesis remains that the average adult who is healthy has temperature of 98.6 degrees. We do not prove that this is true.
Null Hypothesis and Alternative Hypothesis."
If we are studying a new treatment, the null hypothesis is that our treatment will not change our subjects in any meaningful way. In other words, the treatment will not produce any effect in our subjects.