There is a new ultrasound system that will be marketed to hospitals. The company
ID: 3352114 • Letter: T
Question
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. (a) State 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
The given hypothesis is by using new ultrasound system,it will detect more Type q tumour in early stages than old technology.
By using testing of hypothesis we have to conclude the hypothesis by accepting or rejecting the hypothesis.
Type -I error means, rejecting the true condition. Identified with level of siginificance .
For the given hypothesis, we may produce bad report for tumour case in case of positive case.This may tends to Type I error.
Type-II error means, we may accept the hypothesis which produces negative impact on the hypocrite.Which is identified with most powerful test.
From the given hypothesis we may produce non tumour result for pure tumour case's.
Increasing the sample size decreases the likely difference between the true population mean and the mean of your sample.
As with a small sample size , high variance of the hospital can make your sample mean more different from the true population mean.
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