what is a null hypothesis 
a null hypothesis is a type of statistical hypothesis that proposes that no statistical significance exists in a set of given observations hypothesis testing is used to assess the credibility of a hypothesis by using sample data sometimes referred to simply as the null it is represented as h0 the null hypothesis also known as the conjecture is used in quantitative analysis to test theories about markets investing strategies and economies to decide if an idea is true or false alex dos diaz investopediaunderstanding a null hypothesisa gambler may be interested in whether a game of chance is fair if it is then the expected earnings per play come to zero for both players if it is not then the expected earnings are positive for one player and negative for the other to test whether the game is fair the gambler collects earnings data from many repetitions of the game calculates the average earnings from these data then tests the null hypothesis that the expected earnings are not different from zero if the average earnings from the sample data are sufficiently far from zero then the gambler will reject the null hypothesis and conclude the alternative hypothesis namely that the expected earnings per play are different from zero if the average earnings from the sample data are near zero then the gambler will not reject the null hypothesis concluding instead that the difference between the average from the data and zero is explainable by chance alone a null hypothesis can only be rejected not proven the null hypothesis assumes that any kind of difference between the chosen characteristics that you see in a set of data is due to chance for example if the expected earnings for the gambling game are truly equal to zero then any difference between the average earnings in the data and zero is due to chance analysts look to reject the null hypothesis because doing so is a strong conclusion this requires evidence in the form of an observed difference that is too large to be explained solely by chance failing to reject the null hypothesis that the results are explainable by chance alone is a weak conclusion because it allows that while factors other than chance may be at work they may not be strong enough for the statistical test to detect them the alternative hypothesisan important point to note is that we are testing the null hypothesis because there is an element of doubt about its validity whatever information that is against the stated null hypothesis is captured in the alternative alternate hypothesis h1 1for the examples below the alternative hypothesis would be in other words the alternative hypothesis is a direct contradiction of the null hypothesis null hypothesis exampleshere is a simple example a school principal claims that students in her school score an average of seven out of 10 in exams the null hypothesis is that the population mean is 7 0 to test this null hypothesis we record marks of say 30 students sample from the entire student population of the school say 300 and calculate the mean of that sample we can then compare the calculated sample mean to the hypothesized population mean of 7 0 and attempt to reject the null hypothesis the null hypothesis here that the population mean is 7 0 cannot be proved using the sample data it can only be rejected take another example the annual return of a particular mutual fund is claimed to be 8 assume that the mutual fund has been in existence for 20 years the null hypothesis is that the mean return is 8 for the mutual fund we take a random sample of annual returns of the mutual fund for say five years sample and calculate the sample mean we then compare the calculated sample mean to the claimed population mean 8 to test the null hypothesis for the above examples null hypotheses are for the purposes of determining whether to reject the null hypothesis abbreviated h0 said hypothesis is assumed for the sake of argument to be true then the likely range of possible values of the calculated statistic e g the average score on 30 students tests is determined under this presumption e g the range of plausible averages might range from 6 2 to 7 8 if the population mean is 7 0 2if the sample average is outside of this range the null hypothesis is rejected otherwise the difference is said to be explainable by chance alone being within the range that is determined by chance alone 2