Defining Errors
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AP Statistics › Defining Errors
A prominent football coach is being reviewed for his performance in the past season. To evaluate how well the coach has done, the team manager runs a statistical test comparing the coach to a sample of coaches in the league. If the test suggests that the coach outperformed other coaches when in fact he did not, and the manager then rejects the null hypothesis (that the coach did not outperform the other coaches), what kind of error is he committing?
Type I error
Type II error
Type M error
None of the above
Explanation
A type I error occurs when one rejects a null hypothesis that is in fact true. The null hypothesis is that the coach does not outperform other coaches, and the test reccomends that we reject it even though it is true. Thus, a type I error has been committed.
A prominent football coach is being reviewed for his performance in the past season. To evaluate how well the coach has done, the team manager runs a statistical test comparing the coach to a sample of coaches in the league. If the test suggests that the coach outperformed other coaches when in fact he did not, and the manager then rejects the null hypothesis (that the coach did not outperform the other coaches), what kind of error is he committing?
Type I error
Type II error
Type M error
None of the above
Explanation
A type I error occurs when one rejects a null hypothesis that is in fact true. The null hypothesis is that the coach does not outperform other coaches, and the test reccomends that we reject it even though it is true. Thus, a type I error has been committed.
If a hypothesis test uses a 
Explanation
By definition, the probability of Type I Error is,
where,
Thus resulting in:
If a hypothesis test uses a
Explanation
By definition, the probability of Type I Error is,
where,
Thus resulting in:
A factory claims that only 1% of their widgets are defective but a large amount of their produced widgets have been breaking for customers. A test is conducted to figure out if the factory claim of 1% defective is true or if the customers claim of graeater than 1% is true. What would be an example of a Type II error?
The test shows that only 1% are defective when the truth is that more than 1% are defective. The null is upheld when it should be rejected.
The test shows that there are more than 1% defective even though the null of just 1% is actually true.
The test came up with no definitive answer.
The test shows that the percentage of defective widgets is 1% and the factory claim is upheld.
More than 1% are shown to be defective and the reject the factory claim of only 1% defective.
Explanation
Type II Error is not rejecting a truly false null hypothesis. This means that the test supports the factory claim of 1% even though the true amount is more than that.
A factory claims that only 1% of their widgets are defective but a large amount of their produced widgets have been breaking for customers. A test is conducted to figure out if the factory claim of 1% defective is true or if the customers claim of graeater than 1% is true. What would be an example of a Type II error?
The test shows that only 1% are defective when the truth is that more than 1% are defective. The null is upheld when it should be rejected.
The test shows that there are more than 1% defective even though the null of just 1% is actually true.
The test came up with no definitive answer.
The test shows that the percentage of defective widgets is 1% and the factory claim is upheld.
More than 1% are shown to be defective and the reject the factory claim of only 1% defective.
Explanation
Type II Error is not rejecting a truly false null hypothesis. This means that the test supports the factory claim of 1% even though the true amount is more than that.
You and a friend wanted to test the effect of similar servings of juice and soda on blood sugar levels.
Your friend told you that they found the null hypothesis valid, which was what there is no difference between the effects of similar servings of juice and soda on blood sugar levels.
If the null hypothesis was actually false, what type of error was made?
Type II
Type I
Type I and II
Neither
Explanation
A type I error occurs when the null hypothesis is valid but rejected.
A type II error occurs when the null hypothesis is false, but fails to be rejected.
Because the null hypothesis was false, but had failed to be rejected, they made a Type II error.
You and a classmate wanted to test the effect of sugars and fats on levels of blood sugar.
Your classmate told you that they found the null hypothesis valid, which was what there is no difference between the effects of sugars and fats on blood sugar levels.
If the null hypothesis was actually false, what type of error was made?
Type II
Type I
Type I and II
Neither
Explanation
A type I error occurs when the null hypothesis is valid but rejected.
A type II error occurs when the null hypothesis is false, but fails to be rejected.
Because the null hypothesis was false, but had failed to be rejected, they made a Type II error.
You and a friend wanted to test the effect of similar servings of juice and soda on blood sugar levels.
Your friend told you that they found the null hypothesis valid, which was what there is no difference between the effects of similar servings of juice and soda on blood sugar levels.
If the null hypothesis was actually false, what type of error was made?
Type II
Type I
Type I and II
Neither
Explanation
A type I error occurs when the null hypothesis is valid but rejected.
A type II error occurs when the null hypothesis is false, but fails to be rejected.
Because the null hypothesis was false, but had failed to be rejected, they made a Type II error.
If a test has a power of 
Explanation
From the statistical definition of power (of a test), the power is equal to 
Therefore our equation to solve becomes:
