Question

A patient named Diana was diagnosed with Fibromyalgia, a long-term syndrome of body pain, and was prescribed anti-depressants. Being the skeptic that she is, Diana didn't initially believe that antidepressants would help her symptoms. However after a couple months of being on the medication she concludes that the antidepressants are working, because she feels that her symptoms are in fact getting better.

Answer 1

SOLUTION:

From the above information we can find out the three things.

a)

We know that the null hypothesis is the hypothesis of no difference.
Therefore the null hypothesis in this case here i.e. when Diana started taking the anti-depressents is given by ,

Ho : The effect of anti-depressents on Diana's symptoms being skeptic was insignificant .

[ i.e. there was no effect of the anti-depressents on Diana's disease ]

And the alternative hypothesis is given by,

Ha : The effect of anti-depressants on Diana's symptoms was significant .

[ There was a significant effect of the anti-depressants on the Diana's treatment ]

b.)

We know that type 1 error occurs when the null hypothesis is rejected and it is true .

[ i.e. rejection of true null hypothesis ]

In the context type 1 Error would occur when we will accept that the anti-depressants have an effect on the disease of Diana i.e. we accept Ha and reject Hoand thus they significantly contribute to better Diana's symptoms but in reality there will not be any such kind of improvement in Diana's Health due to any working of the Anti-depressants.

[ i.e. We reject Ho even if it is true ]

c.)

We know that type 2 error occurs when we accept the null hypothesis even when it is false .

Here we would come across type 2 error when we would accept and believe that the medicines given to Diana did not worked and helped her in getting her symptoms better but actually this is not true . The anti depressants contributed significantly towards Diana's symptoms and worked even after being skeptical. Here the situation supports the alternative hypothesis but we accept the null hypothesis and type 2 error comes into existence in this scenario.

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