Fundamentals of Hypothesis-Testing Methodology
Fundamentals of Hypothesis-Testing Methodology
Hypothesis testing typically begins with a theory, a claim, or an assertion about a particular parameter of a population.
Some of them are:
• The Null and Alternative Hypotheses
The hypothesis that the population parameter is equal to the company specification is referred to as the null hypothesis. A null hypothesis is often one of status quo and is identified by the symbol H0. Whenever a null hypothesis is specified, an alternative hypothesis is also specified, and it must be true if the null hypothesis is false. The alternative hypothesis H1, is the opposite of the null hypothesis H0. The alternative hypothesis represents the conclusion reached by rejecting the null hypothesis. The null hypothesis is rejected when there is sufficient evidence from the sample data that the null hypothesis is false.
• Regions of Rejection and Non-rejection
The sampling distribution of the test statistic is divided into two regions, a region of rejection (sometimes called the critical region) and a region of non-rejection. If the test statistic falls into the region of non-rejection, you do not reject the null hypothesis. The region of rejection consists of the values of the test statistic that are unlikely to occur if the null hypothesis is true. These values are much more likely to occur if the null hypothesis is false. Therefore, if a value of the test statistic falls into this rejection region, you reject the null hypothesis because that value is unlikely if the null hypothesis is true.
To make a decision concerning the null hypothesis, you first determine the critical value of the test statistic. The critical value divides the non-rejection region from the rejection region. Determining the critical value depends on the size of the rejection region. The size of the rejection region is directly related to the risks involved in using only sample evidence to make decisions about a population parameter.
• Risks in
Hypothesis testing typically begins with a theory, a claim, or an assertion about a particular parameter of a population.
Some of them are:
• The Null and Alternative Hypotheses
The hypothesis that the population parameter is equal to the company specification is referred to as the null hypothesis. A null hypothesis is often one of status quo and is identified by the symbol H0. Whenever a null hypothesis is specified, an alternative hypothesis is also specified, and it must be true if the null hypothesis is false. The alternative hypothesis H1, is the opposite of the null hypothesis H0. The alternative hypothesis represents the conclusion reached by rejecting the null hypothesis. The null hypothesis is rejected when there is sufficient evidence from the sample data that the null hypothesis is false.
• Regions of Rejection and Non-rejection
The sampling distribution of the test statistic is divided into two regions, a region of rejection (sometimes called the critical region) and a region of non-rejection. If the test statistic falls into the region of non-rejection, you do not reject the null hypothesis. The region of rejection consists of the values of the test statistic that are unlikely to occur if the null hypothesis is true. These values are much more likely to occur if the null hypothesis is false. Therefore, if a value of the test statistic falls into this rejection region, you reject the null hypothesis because that value is unlikely if the null hypothesis is true.
To make a decision concerning the null hypothesis, you first determine the critical value of the test statistic. The critical value divides the non-rejection region from the rejection region. Determining the critical value depends on the size of the rejection region. The size of the rejection region is directly related to the risks involved in using only sample evidence to make decisions about a population parameter.
• Risks in