For each of the following hypothetical analyses, decide whether the appropriate test is binomial, goodness of fit, or independence. Then give the appropriate null and alternative hypothesis in words. (Note that binomial tests can be considered a special form of GOF, but if the binomial test can be performed, call it binomial and render the null and alternative hypotheses in symbols, instead.) a) Respondents to a survey indicate whether they Agree, Disagree, or Don’t Know that a carbon tax would help reduce greenhouse gas emissions. A researcher wants to know if such opinions are affected by what political party people belong to. b) At hospital births, the attendant rates the newborn 1 minute after birth with a number called the Apgar score, on a scale of 1 to 10. Scores of 7 or above are considered normal, and scores of 6 or below indicate that babies need immediate medical attention, such as airway clearance. Suppose you wish to test the proposition that the race of the mother does not matter to whether babies get normal or non-normal Apgar scores. c) St. Wigglebum’s Hospital has a goal that no more than 10 percent of non-Caesarean births will result in Apgar scores in the “needs medical attention” category. You plan to take a large sample to see if the hospital is meeting that standard. d) Some butterfly species lay their eggs on the underside of leaves, while others lay their eggs on the topsides. There may be advantages and disadvantages to both strategies, but researchers wonder if, in general, one strategy is superior (and therefore significantly more common among butterfly species). A sample of 84 butterfly species is analyzed. e) Among the U.S. population, blood types O, A, B, and AB are 44.0%, 42.0%, 10.0%,and 4%, respectively. A CDC researcher has health data from a sample of 1,000 people that includes several variables, including blood type. However, the label on the data has been lost and the researcher is not sure if the data are from the U.S. or not. How can she test to see if her data are likely to be Americans?
For each of the following hypothetical analyses, decide whether the appropriate test is binomial, goodness of fit, or independence. Then give the appropriate null and alternative hypothesis in words. (Note that binomial tests can be considered a special form of GOF, but if the binomial test can be performed, call it binomial and render the null and alternative hypotheses in symbols, instead.)
a) Respondents to a survey indicate whether they Agree, Disagree, or Don’t Know that a carbon tax would help reduce greenhouse gas emissions. A researcher wants to know if such opinions are affected by what political party people belong to.
b) At hospital births, the attendant rates the newborn 1 minute after birth with a number called the Apgar score, on a scale of 1 to 10. Scores of 7 or above are considered normal, and scores of 6 or below indicate that babies need immediate medical attention, such as airway clearance. Suppose you wish to test the proposition that the race of the mother does not matter to whether babies get normal or non-normal Apgar scores.
c) St. Wigglebum’s Hospital has a goal that no more than 10 percent of non-Caesarean births will result in Apgar scores in the “needs medical attention” category. You plan to take a large sample to see if the hospital is meeting that standard.
d) Some butterfly species lay their eggs on the underside of leaves, while others lay their eggs on the topsides. There may be advantages and disadvantages to both strategies, but researchers wonder if, in general, one strategy is superior (and therefore significantly more common among butterfly species). A sample of 84 butterfly species is analyzed.
e) Among the U.S. population, blood types O, A, B, and AB are 44.0%, 42.0%, 10.0%,and 4%, respectively. A CDC researcher has health data from a sample of 1,000 people that includes several variables, including blood type. However, the label on the data has been lost and the researcher is not sure if the data are from the U.S. or not. How can she test to see if her data are likely to be Americans?
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