The director of an advertising agency is concerned with the effectiveness of a television commercial.
What null hypothesis is she testing if she commits a type I error when she
erroneously says that the commercial is effective.
Null hypotheses propose no effect.
The director of an advertising agency is concerned with the effectiveness of a television commercial.
- What null hypothesis is she testing if she makes a correct decision when she says that the commercial is not effective?
To understand the null hypothesis being tested in this scenario, we need to break down the problem and define some key terms.
The null hypothesis, denoted as H₀, represents the statement of no effect or no difference. In the context of the director's concern with the commercial's effectiveness, the null hypothesis can be formulated as follows:
H₀: The television commercial is not effective.
Based on this statement, the director is testing whether there is no significant effect of the television commercial on consumers' behavior, perceptions, or preferences.
Now, let's discuss the concept of type I error. A type I error occurs when the null hypothesis is incorrectly rejected, meaning that a significant effect is concluded when, in reality, there is no effect.
Considering the question, if the director erroneously says that the commercial is effective, it means she falsely rejects the null hypothesis. In other words, she commits a type I error by concluding a significant effect for the commercial when, in fact, there is no such effect.
Therefore, the null hypothesis being tested in this situation, which leads to a type I error when mistakenly rejecting it, is:
H₀: The television commercial is not effective.