Then, we hypothesize that the 's are equal wich is null hypothesis.

Your first task is to turn the claim into algebra. The claimmay be that nothing is going on, or that something is going on. Youalways have two statements, called the null and alternativehypotheses.

If the null hypothesis is true, then the mean is 0.

A Type II error is failing to reject the nullhypothesis when it’s actually false.

Our null hypothesis is that it is not.

The probability that was calculated above, 0.030, is the probability of getting 17 or fewer males out of 48. It would be significant, using the conventional PP=0.03 value found by adding the probabilities of getting 17 or fewer males. This is called a one-tailed probability, because you are adding the probabilities in only one tail of the distribution shown in the figure. However, if your null hypothesis is "The proportion of males is 0.5", then your alternative hypothesis is "The proportion of males is different from 0.5." In that case, you should add the probability of getting 17 or fewer females to the probability of getting 17 or fewer males. This is called a two-tailed probability. If you do that with the chicken result, you get P=0.06, which is not quite significant.

An Application: Suppose we wish to test the null hypothesis

The P-value approach involves determining "likely" or "unlikely" by determining the probability — assuming the null hypothesis were true — of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed. If the P-value is small, say less than (or equal to) α, then it is "unlikely." And, if the P-value is large, say more than α, then it is "likely."

Let  be such that:    is an alternative to represent departure from the null hypothesis.

Why fail to reject rather than accept null.

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.

Learn About Null Hypothesis and Alternative Hypothesis

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 egg-laying 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 chocolate-fed 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.

which we fail to reject the null hypothesis

Remark:C is wrong because “model good” is H0. D isalso wrong: every hypothesis test, without exception, compares ap-value to α. For E, df is number of cells minus 1. F isbackward: in every hypothesis test you reject H0 when your sample is veryunlikely to have occurred by random chance.

value is less than 0.05, you reject the null hypothesis; ..

The null hypothesis, symbolH0, is the statement that nothing is going on, that there is noeffect, “nothin’ to see here. Move along, folks!” Itis an equation, saying that , the proportion in the population(which you don’t know), equals some number.

to reject a null hypothesis rather than trying ..

There are different ways of doing statistics. The technique used by the vast majority of biologists, and the technique that most of this handbook describes, is sometimes called "frequentist" or "classical" statistics. It involves testing a null hypothesis by comparing the data you observe in your experiment with the predictions of a null hypothesis. You estimate what the probability would be of obtaining the observed results, or something more extreme, if the null hypothesis were true. If this estimated probability (the P value) is small enough (below the significance value), then you conclude that it is unlikely that the null hypothesis is true; you reject the null hypothesis and accept an alternative hypothesis.