Statistical Hypothesis Testing: A Comprehensive Guide for Business Students, Lecture notes of Statistics

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STATISTICS FOR BUSINESS

II

Doç. Dr. Yüksel Akay ÜNVAN

STATISTICAL HYPOTHESIS TESTING

A statistical hypothesis is a statement about a population parameter. A

parameter is a value that defines the characteristic of a whole population

which means that population parameter consists of mean, variance,

standard deviation, mode, median or proportion of the population or

objects under consideration. Researchers and scientists in various areas for

instance business, marketing, medicine, agriculture and education utilize

hypothesis testing to make decisions about the population parameters

based on sample information.

STATISTICAL HYPOTHESIS TESTING In general, a hypothesis is a proposition for the specific situation encountered. Conversely a statistical hypothesis that specifies a single value for a population parameter and validity of this parameter is based on generating statistics which can be investigated by sampling distribution of the concerned information. In other words, statistical hypothesis utilizes sample statistics to determine whether a hypothesis is true or not. Some examples of statistical hypotheses are given as follows:

• The mean age of students in a classroom is 26.5 years.
• The proportion of people wearing eyeglasses is almost four times higher than

STATISTICAL HYPOTHESIS TESTING To test the claims made about the population parameters or in other words to test the statistical expressions the following steps can be followed: Step 1: State null and alternate hypotheses Step 2: Select a level of significance Step 3: Identify the test statistic Step 4: Formulate a decision rule Step 5: Take a sample and make the decision Let’s now explain these steps in detail as follows.

STATE THE NULL AND ALTERNATE HYPOTHESES Alternative hypothesis is also called as research hypothesis since the alternative hypothesis defines what the decision maker’s conclusion is if he/she rejects the null hypothesis. Besides that, if the alternative hypothesis is accepted, this means that the sample data supplies enough statistical information that the null hypothesis is false. If the null hypothesis is not rejected on the basis of the sample data, this does not mean that the null hypothesis is actually true.

If the main research objective is deciding whether a population parameter, θ, is different from a specified value of θ 0 , then the alternative hypothesis (H 1 ) can be written in the following form. H 1 : θ ≠ θ 0 A hypothesis test whose alternative hypothesis (H 1 ) has this form named as the two-tailed test or two sided alternative hypothesis. If the main research objective is deciding whether a population parameter, θ, is greater than from a specified value of θ 0 , then the alternative hypothesis (H 1 ) can be written in the following form.

TESTS OF HYPOTHESES: MEANS