# A small (p)-valueis an indication that the null hypothesis is false.

This number, 0.030, is the P value. It is defined as the probability of getting the observed result, or a more extreme result, if the null hypothesis is true. So "P=0.030" is a shorthand way of saying "The probability of getting 17 or fewer male chickens out of 48 total chickens, IF the null hypothesis is true that 50% of chickens are male, is 0.030."

## Five Steps in a Hypothesis Test

### What a p-Value Tells You about Statistical Data

Lastly, we need to set the "alpha value" which can be viewed as a "threshold for acceptance." Common values are .05, .01, and .001. With an alpha value of .05, there is a 95% chance your results are correct. With a value of .01, there is a 99% chance your results are correct, and so on. . . You can never have an alpha value of zero, because you can never be 100% confident of anything in statistics (this is not a joke).

### Null and Alternative Hypotheses for a Mean

The good news is that, whenever possible, we will take advantage of the test statistics and P-values reported in statistical software, such as Minitab, to conduct our hypothesis tests in this course.

## Use the following formula to calculate your test value.

Before we can begin to crunch some numbers, we must clearly define our null and alternative hypothesis. You may be asking why we need two hypotheses for a statistical test. In formal statistics, we always compare two hypotheses, the null and alternative.

## Since the p-value ll hypothesis with an alpha value of 0.05.

The p-value is the probability that a t-value would be greater than (to the right of ) 4.03. From Minitab we get 0.001. If using we would look at DF = 9 and since t = 4.03 > 3.00 our p-value from the table would p

## Use the following formula to calculate your test value.

The T-test is powerful, because it allows us to make inferences from a small sample size about the whole population. We will show you how to do a T-test for the first hypothesis, but it will be up to you to perform the T-test for the second hypothesis.

### "Hypothesis Testing."From --A Wolfram Web Resource.

Someone came up with a simpler approach to this problem that can be summed up as follows: what are the chances that you get the same result by pure chance? If these chances (known as the p-value of the test) are low enough then we could reject the idea of pure chance, thus confirming that in the trial something was killing bacteria. This is NHST: if we can reject the null hypothesis of pure chance with a good degree of significance then the alternate hypothesis of something going on is selected as a better explanation of the evidence.

### Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

Imagine that you manage a lab and you need to test if a newly developed antibiotic drug kills bacteria. The trial seems straightforward: you put some of the new drug into a Petri dish with the bacteria and you wait to see if it works (also, apologies for my ignorance on lab trials to any lab technician that could be listening…). Your working hypothesis is that the drug is effective and kills bacteria, so what are the possible outcomes?

### Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

If your test statistic is positive, first find the probability that is greater than your test statistic (look up your test statistic on the -table, find its corresponding probability, and subtract it from one). Then double this result to get thevalue.