# UNDERSTANDING HYPOTHESIS TESTING WITH ONE SAMPLE

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One job of a statistician is to make statistical inferences about populations based on samples taken from the population.

Confidence intervals are one way to estimate a population parameter.

Another way to make a statistical inference is to make a decision about a parameter.

For instance, a car dealer advertises that its new small truck gets 35 miles per gallon, on average. A tutoring service claims that its method of tutoring helps 90% of its students get an A or a B. A company says that women managers in their company earn an average of \$60,000 per year.

A statistician will make a decision about these claims. This process is called ” hypothesis testing.”

A hypothesis test involves collecting data from a sample and evaluating the data.

Then, the statistician makes a decision as to whether or not there is sufficient evidence, based upon analyses of the data, to reject the null hypothesis.

In this article, you will conduct hypothesis tests on single means and single proportions. You will also learn about the errors associated with these tests.

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.

Contents

### Null and Alternative Hypothesis

The actual test begins by considering two hypotheses. They are called the null hypothesis and the alternative hypothesis.

These hypotheses contain opposing viewpoints.
H0: The null hypothesis:

It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.

Ha: The alternative hypothesis: It is a claim about the population that is contradictory to H0 and what we conclude when we reject H0.

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision.

They are “reject H0” if the sample information favors the alternative hypothesis or “do not reject H0” or “decline to reject H0” if the sample information is insufficient to reject the null hypothesis.

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