## Example 11.2. Hypotheses with One Sample of One Categorical Variable

In an effort to improve the world we live in, all it takes is an initial hypothesis that is well-stated, founded in truth, and can withstand extensive research and experimentation. As it turns out, despite its incredible explanatory power, newton's hypothesis was wrong," says dave. Therefore, you would conduct your research using a statistical hypothesis, or a sample of the savannian ters of a good order for a hypothesis to be sound, hold tight to these tips:Ask yourself torm.

The null hypothesis is essentially the "devil's advocate" position. That is, it assumes that whatever you are trying to prove did not happen (*hint:* it usually states that something equals zero). For example, the two different teaching methods did not result in different exam performances (i.e., zero difference). Another example might be that there is no relationship between anxiety and athletic performance (i.e., the slope is zero). The alternative hypothesis states the opposite and is usually the hypothesis you are trying to prove (e.g., the two different teaching methods did result in different exam performances). Initially, you can state these hypotheses in more general terms (e.g., using terms like "effect", "relationship", etc.), as shown below for the teaching methods example:

## A better way to write a hypotheses is to use a formalized hypotheses

All of these are examples of hypotheses because they use the tentative word "may." However, their form in not particularly useful. Using the word does not suggest how you would go about proving it. If these statements had not been written carefully, they may not have been a hypotheses at all.

## State Null and Alternative Hypotheses

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## State Null and Alternative Hypotheses

Interpretation of the *p*-value. The likelihood of getting our test statistic of 2.67 or any higher value, if in fact the null hypothesis is true, is 0.004.

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These examples contain the words, if and then. Formalized hypotheses contain two variables. One is "independent" and the other is "dependent." The independent variable is the one you, the scientist control and the dependent variable is the one that you observe and/or measure the results.

## The null hypothesis is a hypothesis which the researcher ..

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.

## The null hypothesis and the alternate ..

Since the *p*-value of 0.004 is so small, the null hypothesis provides a very poor explanation of the data. We find good evidence that the population proportion of left-handed students in the College of Art and Architecture exceeds 0.10.