Question

Explain the influence of a level of significance and sample size has on hypothesis testing. Provide an example of the influence and how it impacts business decisions.

Answer 1

Social science research, and by extension business research, uses a number of different approaches to study a variety of issues. This research may be a very informal, simple process or it may be a formal, somewhat sophisticated process. Regardless of the type of process, all research begins with a generalized idea in the form of a research question or a hypothesis. A research question usually is posed in the beginning of a research effort or in a specific area of study that has had little formal research. A research question may take the form of a basic question about some issue or phenomena or a question about the relationship between two or more variables. For example, a research question might be: "Do flexible work hours improve employee productivity?" Another question might be: "How do flexible hours influence employees' work?"

A hypothesis differs from a research question; it is more specific and makes a prediction. It is a tentative statement about the relationship between two or more variables. The major difference between a research question and a hypothesis is that a hypothesis predicts an experimental outcome. For example, a hypothesis might state: "There is a positive relationship between the availability of flexible work hours and employee productivity."

Hypotheses provide the following benefits:

They determine the focus and direction for a research effort.

Their development forces the researcher to clearly state the purpose of the research activity.

They determine what variables will not be considered in a study, as well as those that will be considered.

They require the researcher to have an operational definition of the variables of interest.

The worth of a hypothesis often depends on the researcher's skills. Since the hypothesis is the basis of a research study, it is necessary for the hypothesis be developed with a great deal of thought and contemplation. There are basic criteria to consider when developing a hypothesis, in order to ensure that it meets the needs of the study and the researcher. A good hypothesis should:

Have logical consistency. Based on the current research literature and knowledge base, does this hypothesis make sense?

Be in step with the current literature and/or provide a good basis for any differences. Though it does not have to support the current body of literature, it is necessary to provide a good rationale for stepping away from the mainstream.

Be testable. If one cannot design the means to conduct the research, the hypothesis means nothing.

Be stated in clear and simple terms in order to reduce confusion.

As previously noted, one can reject a null hypothesis or fail to reject a null hypothesis. A null hypothesis that is rejected may, in reality, be true or false. Additionally, a null hypothesis that fails to be rejected may, in reality, be true or false. The outcome that a researcher desires is to reject a false null hypothesis or to fail to reject a true null hypothesis. However, there always is the possibility of rejecting a true hypothesis or failing to reject a false hypothesis.

Rejecting a null hypothesis that is true is called a Type I error and failing to reject a false null hypothesis is called a Type II error. The probability of committing a Type I error is termed α and the probability of committing a Type II error is termed β. As the value of α increases, the probability of committing a Type I error increases. As the value of β increases, the probability of committing a Type II error increases. While one would like to decrease the probability of committing of both types of errors, the reduction of α results in the increase of β and vice versa. The best way to reduce the probability of decreasing both types of error is to increase sample size.

The probability of committing a Type I error, α, is called the level of significance. Before data is collected one must specify a level of significance, or the probability of committing a Type I error (rejecting a true null hypothesis). There is an inverse relationship between a researcher's desire to avoid making a Type I error and the selected value of α; if not making the error is particularly important, a low probability of making the error is sought. The greater the desire is to not reject a true null hypothesis, the lower the selected value of α. In theory, the value of α can be any value between 0 and 1. However, the most common values used in social science research are .05, .01, and .001, which respectively correspond to the levels of 95 percent, 99 percent, and 99.9 percent likelihood that a Type I error is not being made. The tradeofffor choosing a higher level of certainty (significance) is that it will take much stronger statistical evidence to ever reject the null hypothesis

EXAMPLE.

XYZ Corporation is a company that is focused on a stable workforce that has very little turnover. XYZ has been in business for 50 years and has more than 10,000 employees. The company has always promoted the idea that its employees stay with them for a very long time, and it has used the following line in its recruitment brochures: "The average tenure of our employees is 20 years." Since XYZ isn't quite sure if that statement is still true, a random sample of 100 employees is taken and the average age turns out to be 19 years with a standard deviation of 2 years. Can XYZ continue to make its claim, or does it need to make a change?

State the hypotheses.
H 0 = 20 years
H 1 ≠ 20 years

Determine the test statistic. Since we are testing a population mean that is normally distributed, the appropriate test statistic is:

Specify the significance level. Since the firm would like to keep its present message to new recruits, it selects a fairly weak significance level (α = .05). Since this is a two-tailed test, half of the alpha will be assigned to each tail of the distribution. In this situation the critical values of Z = +1.96 and −1.96.

State the decision rule. If the computed value of Z is greater than or equal to +1.96 or less than or equal to −1.96, the null hypothesis is rejected.

Calculations.

Reject or fail to reject the null. Since 2.5 is greater than 1.96, the null is rejected. The mean tenure is not 20 years, therefore XYZ needs to change its statement.