1. There is a new ultrasound system that will be marketed to hospitals. The comp
ID: 3352113 • Letter: 1
Question
1. There is a new ultrasound system that will be marketed to hospitals. The company that makes them claims that it detects more Type Q tumors in early stages than the old technology. A hospital would like to test this claim by using one new machine and one old machine, and recording the proportion of (known) tumors detected with each machine. e the hypotheses. (b) What are Type I and Type II Errors in the context of the problem? (c) What are the possible consequences of these errors? (d) Discuss the merits of high or low test size, from the hospital's point of view, based on a comparison of the consequences of the Type I and Type II Errors. (e) Would the CEO of the company building the new machine prefer a lower or a higher test size for this study?Explanation / Answer
a) H0 : Detection of type Q tumors is same for both old and new machine
H1 : Detection of type Q tumors is more in new machine than the old one.
b) Type 1 error = Probability that the new machine will detect more type Q tumors when actually the detection power is same for both the machines.
Type 2 error = Probability that both the old and new machines detect type Q tumors at the same rate when actually the detection power is more in the new machine.
c) The consequence of type 1 error is that there will be many false positive case of type Q tumor which will be detected by the new machine but in reality there is no existence of these tumors.
The consequence of type 2 error is that there will be many false negative cases of type Q tumor which will not be detected by the new machine but in reality there is existence of these tumors.
d) If the test size is high, the type 1 error decreases i.e. there is more chance that the null hypothesis is accepted when it is true. It will favour the fact more that the new machine detects more type Q tumors than the old one. If the test size is low, the type 1 error increases and there is more chance that the new machine will detect type Q tumors as much as the old one does. It will make the new machine fallatious.
For type 2 error, as the test size increases, the type 2 error increases i.e. there is more chance that the null hypothesis is accepted when it is false. It will favour the fact more that the new machine detects same amount of type Q tumors as the old one does when the detection power of new machine is more. If the test size is low, the type 2 error decreases and there is more chance that the new machine will detect more type Q tumors than the old one.
e) A lower test size is to be preffered as then the type 2 error decreases and as a consequence, the chance new machine will detect more type Q tumors where it actually occured and do the treatment accordingly.
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