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

A small *p*-value favors the alternative hypothesis. A small *p*-value means the observed data would not be very likely to occur if we believe the null hypothesis is true. So we believe in our data and disbelieve the null hypothesis. An easy (hopefully!) way to grasp this is to consider the situation where a professor states that you are just a 70% student. You doubt this statement and want to show that you are better that a 70% student. If you took a random sample of 10 of your previous exams and calculated the mean percentage of these 10 tests, which mean would be **less likely** to occur if in fact you were a 70% student (the null hypothesis): a sample mean of 72% or one of 90%? Obviously the 90% would be less likely and therefore would have a small probability (i.e. p-value).

Now that you know the null and alternative hypothesis, did you think about what the type 1 and type 2 errors are? It is important to note that Step 1 is before we even collect data. Identifying these errors helps to improve the design of your research study. Let's write them out:

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

In the figure on the left, we see thissituation illustrated graphically. The alternative hypothesis -- your prediction that theprogram will decrease absenteeism -- is shown there. The null must account for the othertwo possible conditions: no difference, or an increase in absenteeism. The figure shows ahypothetical distribution of absenteeism differences. We can see that the term"one-tailed" refers to the tail of the distribution on the outcome variable.

## I’m stuck on how to value the null or alternative hypotheses

In the sample of 100 students listed above, the sample proportion is 18 / 100 = 0.18. The hypothesis test will determine whether or not the null hypothesis that *p* = 0.1 provides a plausible explanation for the data. If not we will see this as evidence that the proportion of left-handed Art & Architecture students is greater than 0.10.

## How to write a null and alternative hypothesis

The p-value is p = 0.236. This is not below the .05 standard, so we do not reject the null hypothesis. Thus it is possible that the true value of the population mean is 72. The 95% confidence interval suggests the mean could be anywhere between 67.78 and 73.06.

## How to write the null and alternative hypothesis

Alternatively to going through these 5 steps by hand we could have invoked Minitab. If you want to try it, open Minitab and go to Stat > Basic Stat > 1- proportion and click Summarize Data and enter 129 for number of trials and 37 for number of events. Next select the checkbox for Perform Hypothesis Test and enter the hypothesized p_{o} value. Finally, the default alternative is "not equal". To select a different alternative click Options and select the proper option from the drop down list next to Alternative, plus click the box for Test and Interval using Normal Approximation. The results of doing so are as follows:

## Writing null hypothesis and alternative ..

If your prediction specifies a direction, and the null therefore is the no differenceprediction and the prediction of the opposite direction, we call this a * one-tailedhypothesis*. For instance, let's imagine that you are investigating the effects ofa new employee training program and that you believe one of the outcomes will be thatthere will be

*less*employee absenteeism. Your two hypotheses might be statedsomething like this:

## 6.6 Difference between Null Hypothesis and Alternative ..

The *p*-value= .004 indicates that we should decide in favor of the alternative hypothesis. Thus we decide that less than 40% of college women think they are overweight.

The "Z-value" (-2.62) is the test statistic. It is a standardized score for the difference between the sample p and the null hypothesis value p = .40. The *p-*value* is* the probability that the z-score would lean toward the alternative hypothesis as much as it does if the true population really was p = .40.