Defining Errors - AP Statistics
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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?
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?
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 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.
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If a hypothesis test uses a 
confidence level, then what is its probability of Type I Error?
If a hypothesis test uses a
By definition, the probability of Type I Error is,
where,
represents Probability of Type I Error and 
represents the confidence level.
Thus resulting in:
By definition, the probability of Type I Error is,
where,
Thus resulting in:
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For significance tests, which of the following is an incorrect way to increase power (the probability of correctly rejecting the null hypothesis)?
For significance tests, which of the following is an incorrect way to increase power (the probability of correctly rejecting the null hypothesis)?
Recall that power is 
. The probability of Type I and Type II errors will change inversely of each other as the probability of making a Type I error changes. If 
increases, then 
decreases, and as a result power will increase. So if 
decreases, 
would increase, and power would decrease; therefore decreasing 
will not increase power.
Recall that power is
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In a recent athletic study, your lab partner told you that they rejected the null hypothesis that the fabric of running shoes has no effect on the wearer's running times.
If the null hypothesis was actually valid, what type of error was made?
In a recent athletic study, your lab partner told you that they rejected the null hypothesis that the fabric of running shoes has no effect on the wearer's running times.
If the null hypothesis was actually valid, what type of error was made?
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 true, but rejected, they made a Type I error.
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 true, but rejected, they made a Type I error.
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In a recent academic study, your lab partner told you that they rejected the null hypothesis that the ionization of water has no effect on the rate of grass growth.
If the null hypothesis was actually valid, what type of error was made?
In a recent academic study, your lab partner told you that they rejected the null hypothesis that the ionization of water has no effect on the rate of grass growth.
If the null hypothesis was actually valid, what type of error was made?
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 true, but rejected, they made a Type I error.
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 true, but rejected, they made a Type I error.
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A company claims that they have 12 ounces of potato chips in each of their bags of chips. A customer complaint is filed that they do not truly contain 12 ounces but actually contain less. A sampling test is conducted to see if the comapny measure is true or not. What would be an example of a Type I error?
A company claims that they have 12 ounces of potato chips in each of their bags of chips. A customer complaint is filed that they do not truly contain 12 ounces but actually contain less. A sampling test is conducted to see if the comapny measure is true or not. What would be an example of a Type I error?
The type I error is rejecting the null hypothesis when it is actually true. The null here is 12 ounces per bag so a type I error would be rejecting the company claim even though there are 12 ounces per bag.
The type I error is rejecting the null hypothesis when it is actually true. The null here is 12 ounces per bag so a type I error would be rejecting the company claim even though there are 12 ounces per bag.
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If a test has a power of 
, what is the probability of Type II error?
If a test has a power of
From the statistical definition of power (of a test), the power is equal to 
where 
represents the Type II error.
Therefore our equation to solve becomes:
From the statistical definition of power (of a test), the power is equal to
Therefore our equation to solve becomes:
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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?
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?
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.
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.
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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?
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?
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.
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.
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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?
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?
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.
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.
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