Support or Reject Null Hypothesis
If you are able to reject the null hypothesis in Step 2, you can replace it with the alternate hypothesis.
the null hypothesis is rejected when it is true b.
The null hypothesis is a statement that you want to test. In general, the null hypothesis is that things are the same as each other, or the same as a theoretical expectation. For example, if you measure the size of the feet of male and female chickens, the null hypothesis could be that the average foot size in male chickens is the same as the average foot size in female chickens. If you count the number of male and female chickens born to a set of hens, the null hypothesis could be that the ratio of males to females is equal to a theoretical expectation of a 1:1 ratio.
In all tests of hypothesis, there are two types of errors that can be committed. The first is called a Type I error and refers to the situation where we incorrectly reject H_{0} when in fact it is true. This is also called a false positive result (as we incorrectly conclude that the research hypothesis is true when in fact it is not). When we run a test of hypothesis and decide to reject H_{0} (e.g., because the test statistic exceeds the critical value in an upper tailed test) then either we make a correct decision because the research hypothesis is true or we commit a Type I error. The different conclusions are summarized in the table below. Note that we will never know whether the null hypothesis is really true or false (i.e., we will never know which row of the following table reflects reality).
the null hypothesis is not rejected when it is false c.
The test statistic for the χ^{2} test of independence involves comparing observed (sample data) and expected frequencies in each cell of the table. The expected frequencies are computed assuming that the null hypothesis is true. The null hypothesis states that the two variables (the grouping variable and the outcome) are independent. The definition of independence is as follows:
In the two independent samples application with a continuous outcome, the parameter of interest in the test of hypothesis is the difference in population means, μ_{1}μ_{2}. The null hypothesis is always that there is no difference between groups with respect to means, i.e.,
the research hypothesis is not rejected when it is false7221
Basically, you reject the null hypothesis when your test value falls into the . There are four main ways you’ll compute test values and either support or reject your null hypothesis. Which method you choose depends mainly on if you have a proportion or a .
If you have a , or are asked to find a pvalue, follow these instructions to support or reject the null hypothesis. This method works if you are given an and if you are not given an alpha level. If you are given a , just subtract from 1 to get the alpha level. See: .
Alternate Hypothesis Testing: (H1): μ1≠ μ2

# to reject or not to reject the null hypothesis
Formal hypothesis testing requires the formulation of null and alternative hypotheses involving a population parameter.

Null Hypothesis: Two means are equal
Identify the critical value suitable for conducting a twotail test of the hypothesis at the 2% level.

Alternate Hypothesis : Two means are not equal, twotailed testing
When Null Hypothesis is rejected, its complementary statement, the Alternate Hypothesis is true for the given sample.
Null Hypothesis: Two means are equal
The significance level (also known as the "critical value" or "alpha") you should use depends on the costs of different kinds of errors. With a significance level of 0.05, you have a 5% chance of rejecting the null hypothesis, even if it is true. If you try 100 different treatments on your chickens, and none of them really change the sex ratio, 5% of your experiments will give you data that are significantly different from a 1:1 sex ratio, just by chance. In other words, 5% of your experiments will give you a false positive. If you use a higher significance level than the conventional 0.05, such as 0.10, you will increase your chance of a false positive to 0.10 (therefore increasing your chance of an embarrassingly wrong conclusion), but you will also decrease your chance of a false negative (increasing your chance of detecting a subtle effect). If you use a lower significance level than the conventional 0.05, such as 0.01, you decrease your chance of an embarrassing false positive, but you also make it less likely that you'll detect a real deviation from the null hypothesis if there is one.
Alternate Hypothesis : Two means are not equal, twotailed testing
The decision rule is a statement that tells under what circumstances to reject the null hypothesis. The decision rule is based on specific values of the test statistic (e.g., reject H_{0} if Z > 1.645). The decision rule for a specific test depends on 3 factors: the research or alternative hypothesis, the test statistic and the level of significance. Each is discussed below.
failing to reject the null hypothesis when it is false.
Does a probability of 0.030 mean that you should reject the null hypothesis, and conclude that chocolate really caused a change in the sex ratio? The convention in most biological research is to use a significance level of 0.05. This means that if the P value is less than 0.05, you reject the null hypothesis; if P is greater than or equal to 0.05, you don't reject the null hypothesis. There is nothing mathematically magic about 0.05, it was chosen rather arbitrarily during the early days of statistics; people could have agreed upon 0.04, or 0.025, or 0.071 as the conventional significance level.
failing to reject the null hypothesis when it is true.
Notice that the research hypothesis is written in words rather than in symbols. The research hypothesis as stated captures any difference in the distribution of responses from that specified in the null hypothesis. We do not specify a specific alternative distribution, instead we are testing whether the sample data "fit" the distribution in H_{0} or not. With the χ^{2} goodnessoffit test there is no upper or lower tailed version of the test.