11. Quiz: Types of Errors - Part II(b)

Types of Errors - Part II

In the following set of quizzes, you will be doing a recap and combination of the ideas that have been covered so far. Putting all of these pieces together is important for fully understanding hypothesis testing.

Consider we are interested in testing if the average revenue for a new marketing campaign is better than the previous marketing campaign.

We set up the null and alternative hypotheses in the following way:

H_0: \mu_n - \mu_o \leq 0

and

H_1: \mu_n - \mu_o > 0

where \mu_o is the mean revenue of the old campaign, and \mu_n is the mean revenue of the new campaign.

If you were to describe the null hypothesis in words, how would it be stated?
SOLUTION: The null is that the mean revenue of the new campaign is less than or equal to the mean revenue of the old campaign.

If you were to describe the alternative hypothesis in words, how would it be stated?
SOLUTION: The alternative is that the mean revenue of the new campaign is larger than the mean revenue of the old campaign.

QUIZ QUESTION::

Use the setup of the above null and alternative hypotheses to match the error statements to the correct errors.

ANSWER CHOICES:



Statement

Error Type

Deciding the new page is better.

Deciding the old page is better.

Deciding the new page is better, but really the old page is better.

Deciding the old page is better, but really the new page is better.
SOLUTION:

Statement

Error Type

Deciding the new page is better, but really the old page is better.

Deciding the new page is better.

Deciding the old page is better.

Deciding the new page is better.

Deciding the old page is better.

Deciding the old page is better, but really the new page is better.

Let's try another situation. Consider you are testing a new cancer drug to see if it reduces tumor sizes in patients. Let \mu_n be the average reduction in tumor size under the new drug. Let \mu_o be the average reduction in tumor size under the old drug.

We set up the null and alternative hypotheses in the following way:

H_0: \mu_n - \mu_o \leq 0

and

H_1: \mu_n - \mu_o > 0

First, let's map this situation to words.

What does the null hypothesis suggest?
SOLUTION: The old treatment will reduce tumors as well or better than new treatments (on average).

Which of the following statements is another way to state the null hypothesis in this situation?
SOLUTION: The null is that the old drug works as well or better than the new drug.

QUIZ QUESTION::

Use the setup of the above null and alternative hypotheses to match the error statements to the correct errors.

ANSWER CHOICES:



Statement

Error

The new drug is better at reducing tumor sizes.

The old drug is better at reducing tumor sizes.

Based on the study results we decide the new drug is better, but really the old drug is better at reducing tumor sizes.

Based on the study results we decide the old drug is better, but really the new drug is better at reducing tumor sizes.
SOLUTION:

Statement

Error

Based on the study results we decide the old drug is better, but really the new drug is better at reducing tumor sizes.

The new drug is better at reducing tumor sizes.

The old drug is better at reducing tumor sizes.

Based on the study results we decide the new drug is better, but really the old drug is better at reducing tumor sizes.

The new drug is better at reducing tumor sizes.

The old drug is better at reducing tumor sizes.

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