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State the null and alternative hypotheses for a hypothesis test.

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Answer:

In hypothesis testing, the null hypothesis (H0) is a statement that assumes no difference or no effect between two or more variables. The alternative hypothesis (Ha), on the other hand, is a statement that contradicts or challenges the null hypothesis, by asserting that there is a significant difference or effect between the variables being tested.

For example, suppose we want to test whether a new drug is effective in reducing blood pressure in patients. The null and alternative hypotheses would be:

  • Null hypothesis: The new drug has no effect on reducing blood pressure in patients.
  • Alternative hypothesis: The new drug is effective in reducing blood pressure in patients.

In this case, we are testing whether there is a significant difference between the blood pressure of patients who took the new drug and those who did not. The null hypothesis assumes that there is no difference, while the alternative hypothesis suggests that there is a significant difference.

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