In: Statistics and Probability
Please discuss among yourselves if we can prove or disprove a statistical hypothesis. For example, let's say that I have the following null hypothesis: "The population mean is equal to 5", and the alternative hypothesis: "The population mean is not equal to five". Then, I collect a sample from the population and after performing the hypothesis test I conclude at the 0.01 significance level: "Reject the null hypothesis", or in plain English "There is enough evidence to reject the claim that the population mean is equal to five". Then, am I proving that the population mean is not equal to five? Please comment about it and support your assertion (probably you have to do some research on Internet).
Here, H0: miu=5 against H1: miu5
Then we draw a random sample from the given population and find its corresponding test statistic and find its null distribution. Now we check critical value or we calculate p-value and conclude that "Reject the null hypothesis" or simply, "There is enough evidence to reject the claim that the population mean is equal to five."
From the above scenario, we cannot say strictly that "the population mean is not equal to five". Let me explain why.
In testing of hypothesis problem, there is a level of significance, , say 0.05, here. If the null hypothesis is rejected at level , we can only say that the null hypothesis is rejected with 100(1-)% confidence.
Here also in this problem, we reject the null hypothesis at level 0.05,say. So we can conclude that the population mean is not equal to 5, with 95% confidence. We cannot conclude always that the population mean can never be five. This is the difference,