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# IN HYPOTHESIS TESTING, WE HAVE TWO HYPOTHESES: A NULL HYPOTHESIS AND AN ALTERNATIVE HYPOTHESIS

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Author: Christine Farr
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In hypothesis testing, we have two hypotheses: a null hypothesis and an alternative hypothesis. The alternative hypothesis is typically what we wantto demonstrate (based on the research question). We collect data to see if a certain population value differs from a given value (≠), is less than agiven value (<), or is greater than a given value (>). The null hypothesis is typically a baseline or a known standard against which we are testing. Forexample: If we want to test to see if a majority of voters voted for a certain candidate, then our alternative hypothesis would be that the populationproportion who voted for the candidate is greater than 0.50 (i.e. p > 0.50). This is what we want to demonstrate and is the reason for collectingdata. The null hypothesis would be that the population proportion who voted for the candidate is 0.50 (i.e. p = 0.50) which would not be a majority.This is the baseline against which we are testing. Note that the alternative hypothesis covers a range of values, but the null hypothesis is just theone value (i.e. equality).1. A polling group surveyed a city in Scotland regarding residents’ opinions on independence from the UK. It is generally believed that thepercentage of ‘Yes’ votes is 50%. The poll wants to find out whether greater than half (> 50%) of the residents will vote ‘Yes.’ The survey polled 2000residents, of which 1050 responded that they will vote ‘Yes’ on Scotland independence (52.5%). What are the null and alternative hypotheses?A) Null: the percentage of ‘Yes’ votes is 52.5%; Alternative: the percentage of ‘Yes’ votes is greater than 52.5%B) Null: the percentage of ‘Yes’ votes is greater than 52.5%; Alternative: the percentage of ‘Yes’ votes is 52.5%C) Null: the percentage of ‘Yes’ votes is 50%; Alternative: the percentage of ‘Yes’ votes is greater than 50%D) Null: the percentage of ‘Yes’ votes is greater than 50%; Alternative: the percentage of ‘Yes' votes is 50%2. For patients with a particular disease, the population proportion of those successfully treated with a standard treatment that has been used formany years is 0.75. A medical research group invents a new treatment that they believe will be more successful, i.e. the population proportion willexceed 0.75. A doctor plans a clinical trial he hopes will prove this claim. A sample of 100 patients with the disease is obtained. Each person is

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