# Formally we reject the null hypothesis.

This was also a tradeoff between"type I error" and "type II error"; that we do not want to accept the wrong null hypothesis, but we do not want to fail to reject the false null hypothesis, either.

## rejecting a null hypothesis when it is in fact trueb.

### failing to reject a false null hypothesis c.

Back in Chapter 8, you learned the CLT’s:random sample not larger than 10% of population,and at least 10 successes and 10 failures expectedif the null hypothesis is true. You compute expected successes aso by using o, which is the number from H0. Expected failures arethen sample size minus expected successes, −o insymbols. need the samplingdistribution of the proportion to be a , so you must check therequirements as part of your hypothesis test.

### rejecting a false null hypothesis d.

The primary goal of a statistical test is to determine whether an observed data set is so different from what you would expect under the null hypothesis that you should reject the null hypothesis. For example, let's say you are studying sex determination in chickens. For breeds of chickens that are bred to lay lots of eggs, female chicks are more valuable than male chicks, so if you could figure out a way to manipulate the sex ratio, you could make a lot of chicken farmers very happy. You've fed chocolate to a bunch of female chickens (in birds, unlike mammals, the female parent determines the sex of the offspring), and you get 25 female chicks and 23 male chicks. Anyone would look at those numbers and see that they could easily result from chance; there would be no reason to reject the null hypothesis of a 1:1 ratio of females to males. If you got 47 females and 1 male, most people would look at those numbers and see that they would be extremely unlikely to happen due to luck, if the null hypothesis were true; you would reject the null hypothesis and conclude that chocolate really changed the sex ratio. However, what if you had 31 females and 17 males? That's definitely more females than males, but is it really so unlikely to occur due to chance that you can reject the null hypothesis? To answer that, you need more than common sense, you need to calculate the probability of getting a deviation that large due to chance.

## the null hypothesis is rejected when it is true.

When you fail to reject H0, you cannot reach any conclusion.You must use neutral language in your non-conclusions. Please review earlier in this chapter.

### failing to reject the null hypothesis when it is false.

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.

### rejecting the null hypothesis when it is true.

For the goodness-of-fit sample test, we formulate the null and alternative hypothesis as H : fY(y) = fo(y)
H : fY(y) fo(y) At the level of significance, H will be rejected in favor of H if is greater than However, it is possible that in a goodness-of-fit test, one or more of the parameters of fo(y) are unknown.

### rejecting the null hypothesis when the alternative is true.

Leaving the symbols aside, when you test a null hypothesisyour sample either is surprising (and you reject the null hypothesis)or is not surprising (and you fail to reject the null). Any nullhypothesis value inside the confidence interval is close enough toyour sample that it would not get rejected, and any null hypothesisvalue outside the interval is far enough from the sample that it wouldget rejected.