The following information is used for questions 18, 19, 20, 21 and 22: 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. Answer the following questions:

A. Explain in words the statistical meaning of this type of error.
B. Did you realize you were making the error when you reported the results to your boss?
C. What are the business consequences of this error?
D. Give two possible explanations that might explain why you made this error.

a) A Type II error happens when the null hypothesis failed to be rejected even  when the alternative hypothesis is true (false negative).

In this case the ad was effective (true alternative hypothesis), but the results of the sample had no enough statistical evidence to prove that the ad really had an effect increasing sales (reject the null hypothesis).

b) No. This type of errors are not evident, as the study is conduct to infere characteristics of the population. As it is an inference, there is not 100% accurate, and there is a probability of making this type of errors.

The only thing it can be done is limiting the probability of making this errors (type I and type II), affecting the power of the test (to affect Type II error) and the significance level (to affect Type I error). Obviously there is a trade-off, and minimizing one type of error increases the probability of making the other type.

c) The business consequences are that an effective ad campaign is not recognize and a business opportunity is lost. The ad would have been effective, but the study wasn't capable of demostrating its efectiveness.

d) One explanation could be a sample size not big enough. Increasing the sample size increases the power of the test, which decrease the probability of making a Type II error.

Other explanation could be a significance level that was too conservative (very low significance level). That means that the sample result was not considered a unlikely result becuase the threshold for unlikely results was set to a very low probability. This minimizes the probability of making a Type I error, but makes harder for true alternative hypothesis to be demonstrated.

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