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3. Give an example to state the null hypothesis. 4. Assume a trial involves two independent...

3. Give an example to state the null hypothesis.

4. Assume a trial involves two independent tests. What is the complementary event of the event that we would reject one or more of the two null hypotheses?

5. Assume a trial involves two independent tests. Each test is declared statistically significant if p value <0.05. If H0 is true, what is the probability that we would reject one or more of the two null hypotheses?

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Answer #1

3. Null hypothesis is hypothesis of no difference. Suppose you hypothesizes that in the coming exam you will score more marks as compared to the marks scored in previous exam. Therefore here your null hypothesis will be that there is no difference in the marks scored by you in the coming exam i.e. marks scored in previous exam = marks scored in coming exam.

4.Complementary event would be that we would accept both the null hypotheses.

5. Required probability = P(rejecting 1st null hypothesis) + P(rejecting 2nd null hypothesis) + P(rejecting both null hypothesis)

Now, we will reject a null hypothesis when p-value < 0.05

Therefore,  probability that we would reject one or more of the two null hypotheses < 0.05 +0.05 +0.05*0.05 = 0.1025       

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