## Why Say Fail to Reject in a Hypothesis Test? - ThoughtCo

The paired *t*–test is mathematically equivalent to one of the hypothesis tests of a without replication. The paired *t*–test is simpler to perform and may sound familiar to more people. You should use two-way anova if you're interested in testing both null hypotheses (equality of means of the two treatments and equality of means of the individuals); for the horseshoe crab example, if you wanted to see whether there was variation among beaches in horseshoe crab density, you'd use two-way anova and look at both hypothesis tests. In a paired *t*–test, the means of individuals are so likely to be different that there's no point in testing them.

Sometimes, you’ll be given a proportion of the population or a percentage and asked to support or reject null hypothesis. In this case you can’t compute a test value by calculating a (you need actual numbers for that), so we use a slightly different technique.

## Why use a null hypothesis not predicted ..

In the figure above, I used the to calculate the probability of getting each possible number of males, from 0 to 48, under the null hypothesis that 0.5 are male. As you can see, the probability of getting 17 males out of 48 total chickens is about 0.015. That seems like a pretty small probability, doesn't it? However, that's the probability of getting *exactly* 17 males. What you want to know is the probability of getting 17 *or fewer* males. If you were going to accept 17 males as evidence that the sex ratio was biased, you would also have accepted 16, or 15, or 14,… males as evidence for a biased sex ratio. You therefore need to add together the probabilities of all these outcomes. The probability of getting 17 or fewer males out of 48, under the null hypothesis, is 0.030. That means that if you had an infinite number of chickens, half males and half females, and you took a bunch of random samples of 48 chickens, 3.0% of the samples would have 17 or fewer males.

## Hypothesis Testing Why Use Hypotheses in Social …

Further, the standard deviation (i.e., the standard error) of thesampling distribution of the difference between the means must beestimated because the decision to reject the null hypothesis is basedon how many standard error units the observed difference in the samplemeans is from zero.

## 'NULL HYPOTHESIS' is used when testing a research hypothesis.

Instead, the researcher will usually enter the data into computer anduse statistical software that computes the observed t-value andprovides a probability of the observed t-value occurring assuming thenull hypothesis is true.

## Why Use Hypotheses in Social Science Research?

We must assess whether the sample size is adequate. Specifically, we need to check min(np_{0}, np_{1,} ...,np_{k}>) __>__ 5. The sample size here is n=125 and the proportions specified in the null hypothesis are 0.75, 0.25. Thus, min( 125(0.75), 125(0.25))=min(93.75, 31.25)=31.25. The sample size is more than adequate so the formula can be used.

## Why Do Financiers Need Hypothesis Testing

We must assess whether the sample size is adequate. Specifically, we need to check min(np_{0}, np_{1,} ..., n p_{k}) __>__ 5. The sample size here is n=3,326 and the proportions specified in the null hypothesis are 0.02, 0.39, 0.36 and 0.23. Thus, min( 3326(0.02), 3326(0.39), 3326(0.36), 3326(0.23))=min(66.5, 1297.1, 1197.4, 765.0)=66.5. The sample size is more than adequate, so the formula can be used.