Question

You come up with what you think is a great idea for a new advertising campaign for your company. Your boss is worried that the ads will cost a lot of money and she wants to be 99% confident that the ads increase sales before rolling the new ads out nationwide. You run the ads in a typical city and take a random sample to see if people who saw the ad are more likely to buy the product. When you reported the results to your boss, you made a Type II error. 21. Give one possible explanation that might explain why you made this error. (Hint: There are many possible correct answers to this question.)

Answer 1

The type II error might have been committed because of small sample size or small significance level.

Explanation:

A type II error is a statistical word used within the circumstance of hypothesis testing that defines the error that take place when one is unsuccessful to discard a null hypothesis that is truly false. It is symbolized by β i.e.

β = Probability of accepting H₀ when H₀ is false.

In this case we need to test the hypothesis whether the new advertising campaign increases the sales or not.

The hypothesis can be defined as:

H₀: The new advertising campaign does not increases the sales.

Hₐ: The new advertising campaign increases the sales.

The confidence level wanted here is 99%.

The type II error will be made if we conclude that the new advertising campaign does not increases the sales when in fact the sales are increased after the advertising campaign.

The type II error could have been made because of the following reasons:

• The sample size selected is too small. The smaller the sample size, greater is the probability of type II error.
• Significance level of the test must be small. If the significance level is small then the rejection regions decreases. Thus, reducing the chances of correctly rejecting the null hypothesis.

Thus, the type II error might have been committed because of small sample size or small significance level.