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What is a hypothesis?

In science, you may have learned that the hypothesis is an educated guess.  In statistics, the same definition carries over but has some different applications.  A statistical study is similar to the scientific method.  From science you have learned that the scientific method includes the following steps:  1) Ask a question 2) Do background research 3) Construct a hypothesis 4) Test your hypothesis by doing an experiment 5) Analyze the data and draw a conclusion 6) Communicate the results.  In statistics, there are two hypotheses that need to be formed once you have defined the problem and completed background research.  One is called the "null" hypothesis and the other is called the "alternative" hypothesis.  Once the study is conducted, we can reject or fail to reject either of the hypothesis based on the results of the study.The Null HypothesisThe null hypothesis is composed of the fact that there is no effect of the treatment on the subjects in the study.  For example if we were trying to investigate the relationship between two variables our null hypothesis may state that "there is no relationship between the two variables" or if we are trying to see if a new drug has an effect on weight gain the null hypothesis may state that "the drug has no effect on the weight gain of the subjects".  The null hypothesis is the one that we will fail to reject (accept) unless the data provides convincing evidence that it is false.The Alternative HypothesisThe alternative hypothesis may be referred to as the opposite of the null hypothesis.  For example, if the null hypothesis states that there is no relationship between two variables, then the alternative hypothesis should state that "there is a relationship between the two variables that can be measured.  If the null hypothesis states that there is no effect on the subject then the alternative hypothesis should state that "there is an effect on the subject".  We will fail to reject (accept) the alternative hypothesis if and only if the data provides convincing evidence that it is true.  

Practice Writing Null and Alternative Hypotheses

The hypotheses can be written out in words or we may use mathematical symbols to express the hypothesis.  Here a few examples of how to write the null and alternative hypothesis.  The most common symbol for the null hypothesis is H0 and the most common symbol for the alternative hypothesis is H1.Let's Practice:   Case I: An agriculturist is doing a study to determine if a fertilizer has any effect on the average height of 100 apple trees.  He knows that the average height of unfertilized apple trees is 10ft.  The average height of the 100 apple trees that were treated with fertilizer is 10.8 feet with a standard deviation of .5 ft.  

For questions 1-5, write the null and alternative hypothesis.

1.  Does the water temperature have an effect on the number of people in the pool? 2.  Does the weather have an effect on the number of people at the beach? 3.  A fitness center is running a discounted membership fee.  Did the discount increase the membership sales? Write your hypotheses mathematically. 4.  A medical researcher gave 100 patients a new drug to see if it reduces their blood pressure?  Did the new drug reduce the patients' blood pressure?  Write your hypothesis mathematically. 5.  Some students took a conflict resolution class?  Did this class help to reduce the number of conflicts that the students were involved in?  Write your hypothesis mathematically.