Type 1 and Type 2 Error Worksheet For each of the following scenarios complete t
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Question
Type 1 and Type 2 Error Worksheet
For each of the following scenarios complete the following:
Describe a Type 1 error and the consequences of the error.
Describe a Type 2 error and the consequences of the error.
Discuss which type of error is worse.
1. A pharmaceutical company is working on a computerized device for detecting high blood sugar. The patient wears the device all day and the device measures an individual’s blood sugar once per hour at a randomly selected time throughout the day. Then it calculates the mean blood sugar for the 24 measurements. Based on the sample results, the device determines whether there is significant evidence that the individual’s actual mean blood sugar is greater than 200 mg/dL. If so, it recommends that the person see their physician. The hypothesis test performed by the device is:
H0: µ = 200
HA: µ > 200
where µ average blood sugar of the patient.
2. Lexapro is a common drug used to treat depression. One of the side effects of the drug is dry mouth. It is believed that fewer than 5% of patients experience the side effect. A hypothesis test is performed to test the claim
H0: p = 0.10
HA: p < 0.10
where p is the proportion of patients on Lexapro who experience dry mouth.
3. Occasionally, video games are shipped with the disk missing from the box. A consumer advocacy group wants to investigate a claim against a manufacturer of video games brought by a person who claims that the proportion of boxes missing the games is much higher than the value of 0.002 claimed by the manufacturer. A large number of boxes of video games will be tested, and the results will be used to decide between
HO: p = 0.002
HA: p > 0.002
where p represents the true proportion of boxes missing disk made by this manufacturer. If HO is rejected, charges of false advertising will be filed against the manufacturer.
Explanation / Answer
(1)
Type I Error: Rejection of a true Null Hypothesis
Type II Error: Failing to reject a false Null Hypothesis
Suppose in reality mean blood sugar is less than or equal to 200 mg/dL. But, due to Hypothesis testing, we wrongly conclude that mean blood sugar is greater than 200 mg/dL. Type I Error is committed in this case. The consequence of this error is that the person will be uncessarily seeing their physician, which is not at all required.
Suppose in reality mean blood sugar is greater than 200 mg/dL. But, due to Hypothesis testing, we wrongly conclude that mean blood sugar is less than 200 mq/dL. Type II Error is committed in this case. The consequence of this error is that the person will not be seeing thie physician which is required.
Type II error is more serious in this case because the person will not be seeing their phycian which will make the condition of the person bad afterwards.
(2)
Suppose in reality there is no dry mouth. But due to Hypothesis testing, we wrongly conclude that there is dry mouth. Typre I Error is committed in this case. The consequence is that we will be taking corrective actions, which is not at all required.
Suppose in reality there is dry mouth. But due to Hypothesis testing, we wrongly conclude that there is no dry mouth. Type II Error is committed in this case. The consequence is that we will not be taking corrective actions, which is required.
Type II Error is more serious because we will not be taking the nedded corrective actions.
(3) Suppose in reality proportion of boxes missing the game is less than 0.002. But, due to Hypothesis testing, we wrongly conclude that the proportion of boxes missing the game is more than 0.002. Type I Error is committed in this case. The consequence of this error is that unnecessarily charges of false advertising will be filed against the manufacturer.
Suppose in reality proportion of boxes missing the game is greater than 0.002. But due to Hypothesis testing we wrongly conclude that the proportion of boxes is less than 0.002. Type II Error is committed in this case. The consequence of this error is that charges of false advertising will not be filed against the manufacturer, which is reqired.
Type I Error is more serious because charges of false adsvertising will be unnecessarily filed against the manufacturer, which will have grevious consequences at a later date.
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