Decision Rule in Hypothesis Testing

A decision rule is the rule based on which the null hypothesis is rejected or not rejected. We first state the hypothesis. Then we determine if it is a one-tailed or a two tailed test. We then specify a significance level, and calculate the test statistic. Now we calculate the critical value. If the test […]


Test Statistic, Type I and type II Errors, and Significance Level

Test Statistic A test statistic is a quantity, calculated based on a sample, whose value is the basis for deciding whether or not to reject the null hypothesis. In our example, the sample statistic is the mean. Therefore, the test statistic will be: Type I and Type II Error When drawing an inference (from a […]


One-tailed and Two-tailed Hypothesis Tests

A hypothesis test can be a one-tailed or a two-tailed test. A one-tailed test means that the hypothesis is one-sided such as the second and third formulation above. The second formulation tests whether the population parameter is less than a certain value (one-sided). The third formulation tests whether the population parameter is greater than a […]


Null and Alternative Hypothesis

When we form a hypothesis to be tested, the hypothesis is called a null hypothesis. The null hypothesis is written as H0. A null hypothesis will be a simple statement about the population parameter. For example, the hypothesis that the mean returns of a mutual fund will be greater than or equal to 8% will […]


Steps in Hypothesis Testing

The hypothesis testing process consists of the following steps: Stating the hypothesis. Identifying the appropriate test statistic and its probability distribution. Specifying the significance level. Stating the decision rule. Collecting the data and calculating the test statistic. Making the statistical decision.


What is a Hypothesis

Many a times, we want to test the validity of a statement. Consider the following question: Is the mean return from this mutual fund more than the mean return from the benchmark? While answering such a question, our interest is not to find the actual mean returns of the mutual fund, but to test whether […]


Biases in Sampling

As we have seen in this chapter, all our estimates are based on the sample selected from the population. It is therefore critical that we choose the samples correctly so that our results are not biased. That said, there are many issues that could come in that would make our samples biased and lower the […]


How to Read Student’s t Table

Student’s t distribution table has the following structure: The row represents the upper tail area, while the column represents the degrees of freedom. The body contains the t values. Note that for one-tail distribution the values are for a and for two-tailed distribution values are for a/2. Let’s say n = 3, the df= 3-1 […]


Student’s t Distribution

Student’s t distribution, or simply called t-distribution, is a form of continuous probability distributions which is formed when we are trying to estimate the mean of a population that is normally distributed, but we have a small sample size and we don’t know the population standard deviation. When we say that the sample size is […]