Chemotherapy is a standard treatment for certain cancers, and a clinical trial w

Question

Chemotherapy is a standard treatment for certain cancers, and a clinical trial was conducted to test the efficacy of supplementing chemotherapy with immunotherapy (stimulation of the immune system). Combining the two therapies is believed to improve the effectiveness of cancer treatment. Cancer patients in the trial were randomly assigned to receive either chemotherapy only or a combination of both chemotherapy and immunotherapy.

a. State the appropriate null and alternative hypotheses for this study (in words, not symbols).

b. Suppose the null hypothesis was rejected. Which error type would be possible? What would committing this error mean in the context of the study?

c. Suppose the null hypothesis was not rejected. Which error type would be possible? What would committing this error mean in the context of the study?

Explanation / Answer

a.

H0:mu1 less than or equal to mu2 (mean effectiveness of combination of chemotherapy and immunotherapy is less than or equal to  chemotherapy.)

H1:mu1>mu2 (mean effectiveness of combination of chemotherapy and immunotherapy is higher than chemotherapy).

b.

If a true null hypothesis is rejected, the type 1 errror is possible. In this context, it means that effectiveness of combined treatment of chemotherapy and immunotherapy will be counted effective, though it is actually not.

c.

In case of null hypothesis being not rejected, possibility of type II error is evident. In this context a false null hypothesis being accepted. It means that though combination of chemotherapy and immunotherapy is effective, it is not accounted.

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