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# In hypothesis testing, we have two hypotheses, a null hypothesis and an alternative hypothesis. The alternative hypothesis is what we are "testing...

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In hypothesis tesTng, we have two hypotheses, a null hypothesis and an alternaTve hypothesis. ±he alternaTve hypothesis is what we are “tesTng for” (based on the research quesTon). ±his is why we are collecTng data to see if a certain populaTon value diFers from a given value (≠), is less than a given value (<), or is greater than a given value (>). ±he null hypothesis is what we are “tesTng against” which is the given value. ²or example: If we want to test to see if a majority of voters voted for a certain candidate, then our alternaTve hypothesis would be that the populaTon proporTon who voted for the candidate is greater than 0.50 (p > 0.50). ±his is what we are “tesTng for” and collecTng data for. ±he null hypothesis would be that the populaTon proporTon who voted for the candidate is 0.50 (p = 0.50) which would not be a majority. ±his is what we are “tesTng against”. Note that the alternaTve hypothesis covers a range of values, but the null hypothesis is just the one value 1. A polling group surveyed a city in Scotland regarding residents’ opinions on independence from the UK. It is generally believed that the percentage of ‘Yes’ votes is 50%. ±he poll wants to ³nd out whether greater than half (>50%) of the residents will vote ‘Yes’. ±he survey polled 2000 residents, of which 1050 responded that they will vote ‘Yes’ on Scotland independence (52.5%). What are the null and alternaTve hypotheses? A) Null: the percentage of ‘Yes’ votes is 52.5%; AlternaTve: the percentage of ‘Yes’ votes is greater than 52.5% B) Null: the percentage of ‘Yes’ votes is greater than 52.5%; AlternaTve: the percentage of ‘Yes’ votes is 52.5% C) Null: the percentage of ‘Yes’ votes is 50%; AlternaTve: the percentage of ‘Yes’ votes is greater than 50% D) Null: the percentage of ‘Yes’ votes is greater than 50%; AlternaTve: the percentage of ‘Yes' votes is 50% 2. ²or paTents with a parTcular disease, the populaTon proporTon of those successfully treated with a standard treatment that has been used for many years is .75. A medical research group invents a new treatment that they believe will be more successful, i.e., populaTon proporTon will exceed .75. A doctor plans a clinical trial he hopes will prove this claim. A sample of 100 paTents with the disease is obtained. Each person is treated with the new treatment and eventually classi³ed as having either been successfully or not successfully treated with the new treatment. Out of 100 paTents, 80 (80%) were successfully treated by the new treatment. What are the null and alternaTve hypotheses? A) Null: the populaTon proporTon of those successfully treated by the new treatment exceeds .75 (p > . 75); AlternaTve: the populaTon proporTon of those successfully treated by the new treatment is .75 (p = .75) B) Null: the populaTon proporTon of those successfully treated by the new treatment is .75 (p = .75); AlternaTve: the populaTon proporTon of those successfully treated by the new treatment exceeds .75 (p > .75)
C) Null: the populaTon proporTon of those successfully treated by the new treatment is .80 (p = .80); AlternaTve: the populaTon proporTon of those successfully treated by the new treatment exceeds .80 (p > .80) D) Null: the populaTon proporTon of those successfully treated by the new treatment exceeds .80 (p > . 80); AlternaTve: the populaTon proporTon of those successfully treated by the new treatment is .80 (p = .80) 3. Suppose that a study is done comparing two diFerent contact lens we±ng soluTons with regard to hours of wearing comfort. 100 contact lens wearers are randomly divided into two groups. One group uses soluTon A for 2 months. ²he other group uses soluTon B for 2 months. ²he researcher wants to determine if there is a diFerence in the hours of wearing comfort for the two groups. ²he populaTon mean number of hours of wearing comfort will be compared for the two groups. What are the null and alternaTve hypotheses being tested by the researcher? A) Null: there is a diFerence in the populaTon mean number of hours of wearing comfort for the two groups (two populaTon means are not equal); AlternaTve: there is no diFerence in the populaTon mean number of hours of wearing comfort for the two groups (two populaTon means are equal). B) Null: there is no diFerence in the populaTon mean number of hours of wearing comfort for the two groups (two populaTon means are equal); AlternaTve: the populaTon mean from group A is larger than that of group B (populaTon mean group A > populaTon mean group B) C) Null: there is no diFerence in the populaTon mean number of hours of wearing comfort for the two groups (two populaTon means are equal); AlternaTve: there is a diFerence in the populaTon mean number of hours of wearing comfort for the two groups (two populaTon means are not equal) D) Null: the populaTon mean number of hours of wearing comfort for group A is less than that of group B (populaTon mean A < populaTon mean B); AlternaTve: the populaTon mean number of hours of wearing comfort for group B is greater than that of group A (populaTon mean B > populaTon mean A) 4. A car company is tesTng to see if the proporTon of all adults who prefer blue cars has changed (diFers) from .35 since industry staTsTcs indicate this proporTon has been .35 for quite some Tme. A random sample of 1,000 car owners ³nds that the proporTon that prefers blue cars is .40. What are the null and alternaTve hypotheses being tested? A) Null: the populaTon proporTon who prefer blue cars is .35; AlternaTve: the populaTon proporTon who prefer blue cars is greater than .35 B) Null: the populaTon proporTon who prefer blue cars is .40; AlternaTve: the populaTon proporTon who prefer blue cars diFers from (does not equal) .40 C) Null: the populaTon proporTon who prefer blue cars is .40; AlternaTve: the populaTon proporTon who prefer blue cars is greater than .40
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In hypothesis testing, we have two hypotheses, a null hypothesis and an alternative hypothesis. The
alternative hypothesis is what we are “testing for” (based on the research question). This is...

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