Round all answers to at least 3 decimal places. 1. For each of the following sce
ID: 3206433 • Letter: R
Question
Round all answers to at least 3 decimal places.
1. For each of the following scenarios, state the null hypothesis and determine whether the researcher made a Type I Error, a Type II Error, or no error.
a. A fetus is diagnosed with having trisomy 21 even though it has no chromosomal abnormality.
b. A study that tested if there was any relationship between a person’s heart rate and consuming a small amount of caffeine resulted in a p-value of 0.02. In truth, caffeine affects heart rate in this population.
c. A person not infected with HIV receives a negative test result on an HIV test.
d. A new method of relaxation meditation training is reported to be successful at reducing high blood pressure, even though it doesn’t actually have any effect on blood pressure.
e. Park officials tested if a new design of bear-proof trash bins is more successful at keeping bears out than the bins they currently use. Their test resulted in a p-value of 0.13, and the new design is actually more successful than the current one.
Explanation / Answer
Type 1 error : rejecting the null hypothesis when we should not - false positive
Type 2 error : accepting the null hypothesis , when we should not. So keeping this in mind , lets answer the question - false negative
a. A fetus is diagnosed with having trisomy 21 even though it has no chromosomal abnormality.
so this is a false positive case, as we are dignosing a fetus with a disease when it fact it isnt , hence a type1 error
b. A study that tested if there was any relationship between a person’s heart rate and consuming a small amount of caffeine resulted in a p-value of 0.02. In truth, caffeine affects heart rate in this population.
so assuming alpha = 0.05 , as our p value is less than 0.05 hence we would have rejected the null hypothesis in favor of alternate hypothesis to conclude that there is a relationship between the 2 varaibles under consideration. Hence there is no error in this case.
c. A person not infected with HIV receives a negative test result on an HIV test.
so this is a case of false negative , where a person who has HIV got his result as negative. Hence this is a case of type 2 error
d. A new method of relaxation meditation training is reported to be successful at reducing high blood pressure, even though it doesn’t actually have any effect on blood pressure.
This is again false positive or type 1 error , based on pour first statement , we are rejecting the null hypothesis when we shoudnt. Hence a clear case of type 1 error
e. Park officials tested if a new design of bear-proof trash bins is more successful at keeping bears out than the bins they currently use. Their test resulted in a p-value of 0.13, and the new design is actually more successful than the current one.
This is a case of type 2 error , when we are accepting the null hypothesis even though we shoudnt. the new design is actually more successfull then the current design but we are still concluding otherwise , hence a clear case of type 2 error
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