A researcher has developed a new test to be used in diagnosis of early-stage dem

Question

A researcher has developed a new test to be used in diagnosis of early-stage dementia. The test involves a battery of cognitive tests, and is scored on a 100 point scale, with 100 meaning perfect cognitive function. The test is administered to 52 controls subjects, and 48 subjects who are known to have dementia. Then, the distributions of the two groups will be compared to see if the really can distinguish them. 1. [20 pts] What is the null hypothesis for this experiment? Write it out both mathematically and in words. 2. [20 pts] What is the alternative hypothesis? Write it out both mathematically and in words. 3. [15 pts] What would a type-I error look like in this case? 4. [15 pts] What would a type-II error look like? 5. [15 pts] Briefly state your findings, assuming you rejected the null hypothesis. 6. [15 pts] Briefly state your findings, assuming you failed to reject the null hypothesis.

Explanation / Answer

Null hypothesis is there is relationship between two variable .so here null hypothesis is early stage and dementia is no relationship .

H0:u>20

Alternative hypothesis alawys acept the relationship between the two variable.There is significant relationship between early stage and dementia and it is based on real observation.

In the type I error in this case is rejected the true null hypothesis means resercher tries to prove that in early stage dementia can caused.

In type ii error fails to rejected false null hypothesis .that means here when resercher has not able to disapprove that there is no relationship between early stage and dmentia.

Demenia means decline cognitive abilities which is moderately started to show in early stage .so it assumed there is significant relationship between early stage and demenia and this findings rejected the statement of no relationship between them means rejected null hypothesis.

I failed to rejected null hypothesis which caused type two error while level of significant is above 5% .if confidence is less 95% than there is relationship.so data is show above 95% then we fail to rejected null hypothesis

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