9.1: What is a Hypothesis?

A hypothesis can be a simple sentence or statement about a property or any phenomenon observed or predicted for a population. It is usually a claim about a property of the population. It can be stated for any field observations or experiments. A hypothesis statement cannot be said to be right or wrong as it is merely a statement. It needs to be tested through an elaborate data collection process and an appropriate statistical test. A hypothesis should be a general but not a vague statement. It should not be a claim about the population property with a definite number, quantity, or measurement.

A statistician will decide using statistical tests about the claims that proceed the hypothesis statements. This process is called "hypothesis testing." A hypothesis test involves collecting data from a sample and evaluating the data. Then, the statistician decides whether there is sufficient evidence, based upon analyses of the data, to reject the null hypothesis.

Hypothesis testing consists of two contradictory hypotheses or statements, a decision based on the data, and a conclusion. To perform a hypothesis test, a statistician will:

1. Set up two contradictory hypotheses.
2. Collect sample data (in homework problems, the data or summary statistics will be given to you).
3. Determine the correct distribution to perform the hypothesis test.
4. Analyze sample data by performing the calculations that ultimately will allow you to reject or decline to reject the null hypothesis.
5. Make a decision and write a meaningful conclusion.

This text is adapted from Openstax, Introductory Statistics, Section 9 Hypothesis Testing with Open Sample

A hypothesis is a statement about a characteristic or a property of a population. It can be stated as a claim or an idea about some pattern or phenomenon.

A hypothesis is different from a prediction as the hypothesis is a general claim, while a prediction hints toward an exact cause and effect.

The hypothesis is also different from an assumption, which could be a known property of the population that may provide a framework for hypothesis testing.

Consider the statement, 'Red roses attract honeybees.' This is a hypothesis.

In contrast, the statement 'if there are twice the number of red roses, there would be twice the number of honeybees' is considered a prediction. 

Finally, 'honeybees are attracted to all red hues or all sizes of roses equally' is an assumption.

A hypothesis is considered incorrect when it states something that happens by chance alone or when the probability of occurrence is infinitesimally small. 

In statistics, a hypothesis is often stated probabilistically to simplify the process of hypothesis testing.