For several years in the 1990s, Kristen Gilbert worked as a nurse in the intensive care...
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For several years in the 1990s, Kristen Gilbert worked as a nurse in the intensive care unit (ICU) of the Veterans Administration Hospital in Northampton, Massachusetts. Over the course of her time there, other nurses came to suspect that she was killing patients by inject- ing them with the heart stimulant epinephrine. Gilbert was eventually arrested and charged with these murders. Part of the evidence presented against Gilbert at her murder trial was a statistical analysis of 1,641 eight-hour shifts during the time Gilbert worked in the ICU. For each of these shifts, researchers recorded two variables: whether or not Gilbert worked on the shift and whether or not at least one patient died during the shift. I So what did the researchers find when they analyzed the 1,641 eight-hour shifts? They found that Gilbert worked on 257 of the shifts, and she did not work on 1,384 of them. They also found that a patient died during 74 of the shifts, and no death occurred on the other 1,567 shifts. 5. Explain why the information in the previous paragraph does not provide any clues about whether there is an association between Gilbert working on a shift and a patient dying during the shift. What additional information do you need to know? Here is some additional information: Among the 74 shifts during which a patient died, 40 were shifts on which Gilbert worked and 34 were shifts on which Gilbert did not work. 6. Explain why simply comparing only the numbers 40 and 34 is not very informative. When analyzing data on two categorical variables, a useful first step is to organize the data into a two-way table of counts. In this case both variables have only two categories, so we produce a 2 x 2 table. 7. Fill in the missing counts in the following two-way table. (Hint: Start by entering 40 and 34 into the appropriate cells. Then make sure that both rows and both columns add up to the indicated totals.) Patient died during shift No patient died during shift Total Gilbert working on shift 257 Gilbert not working on shift 1,384 Total 74 1,567 1,641 8. Suggest a better way to compare the outcomes of the shifts on which Gilbert worked and the shifts on which she did not work than simply comparing 40 to 34. Explain why your answer is more informative. A next step in analyzing categorical data in a two-way table is to calculate conditional proportions. A conditional proportion simply means that you consider the counts in only one category of the explanatory variable at a time. 9. Now let's calculate the conditional proportions. a. Calculate the conditional proportion of Gilbert shifts on which a patient died. (Hint: Put the total number of Gilbert shifts in the denominator of your fraction.) b. Calculate the conditional proportion of non-Gilbert shifts on which a patient died. For several years in the 1990s, Kristen Gilbert worked as a nurse in the intensive care unit (ICU) of the Veterans Administration Hospital in Northampton, Massachusetts. Over the course of her time there, other nurses came to suspect that she was killing patients by inject- ing them with the heart stimulant epinephrine. Gilbert was eventually arrested and charged with these murders. Part of the evidence presented against Gilbert at her murder trial was a statistical analysis of 1,641 eight-hour shifts during the time Gilbert worked in the ICU. For each of these shifts, researchers recorded two variables: whether or not Gilbert worked on the shift and whether or not at least one patient died during the shift. I So what did the researchers find when they analyzed the 1,641 eight-hour shifts? They found that Gilbert worked on 257 of the shifts, and she did not work on 1,384 of them. They also found that a patient died during 74 of the shifts, and no death occurred on the other 1,567 shifts. 5. Explain why the information in the previous paragraph does not provide any clues about whether there is an association between Gilbert working on a shift and a patient dying during the shift. What additional information do you need to know? Here is some additional information: Among the 74 shifts during which a patient died, 40 were shifts on which Gilbert worked and 34 were shifts on which Gilbert did not work. 6. Explain why simply comparing only the numbers 40 and 34 is not very informative. When analyzing data on two categorical variables, a useful first step is to organize the data into a two-way table of counts. In this case both variables have only two categories, so we produce a 2 x 2 table. 7. Fill in the missing counts in the following two-way table. (Hint: Start by entering 40 and 34 into the appropriate cells. Then make sure that both rows and both columns add up to the indicated totals.) Patient died during shift No patient died during shift Total Gilbert working on shift 257 Gilbert not working on shift 1,384 Total 74 1,567 1,641 8. Suggest a better way to compare the outcomes of the shifts on which Gilbert worked and the shifts on which she did not work than simply comparing 40 to 34. Explain why your answer is more informative. A next step in analyzing categorical data in a two-way table is to calculate conditional proportions. A conditional proportion simply means that you consider the counts in only one category of the explanatory variable at a time. 9. Now let's calculate the conditional proportions. a. Calculate the conditional proportion of Gilbert shifts on which a patient died. (Hint: Put the total number of Gilbert shifts in the denominator of your fraction.) b. Calculate the conditional proportion of non-Gilbert shifts on which a patient died.
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College Mathematics For Business Economics, Life Sciences, And Social Sciences
ISBN: 978-0134674148
14th Edition
Authors: Raymond Barnett, Michael Ziegler, Karl Byleen, Christopher Stocker
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