Statements B and D are outright legit conclusions that can be obtained from the results of this survey while statements A and C, although not outright conclusions, can also be less definite conclusions from the results of the survey.
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Step-by-step explanation:
The complete question as obtained from online is presented in the image attached to this question and also written out here.
Complete Question
Chemicals in butter-flavoring:
Workers in a microwave popcorn production plant in Missouri breathe chemicals that are part of the butter-flavoring. Are these workers at greater risk of developing lung problems? To investigate this question, 135 workers at the plant receive a survey, and 117 respond. Researchers want to compare workers in the popcorn production area with workers who have jobs in other parts of the plant. People in these other jobs are not directly exposed to the butter flavorings.
Of the 97 workers in the production area, 30 reported experiences of "shortness of breath." Of the 20 workers in other jobs, only 1 reported "shortness of breath."
What can we conclude from this study? Check all that apply
a) Since only 117 of the 135 workers in the plant participated in the survey, we must use caution when drawing conclusions.
b) Exposure to the chemicals in butter-flavoring is associated with a greater incidence of lung problems, such as shortness of breath.
c) The chemicals in the butter-flavorings are causing shortness of breath because a much larger percentage of workers in the production area have shortness of breath.
d) Workers exposed to the chemicals in the butter-flavoring have a higher risk of developing respiratory problems such as shortness of breath.
Solution
117 of all the 135 worker respond to the survey. (A large enough percentage to make conclusions for the whole population).
97 of this that responded to the survey worked in the production area and 30 reported shortness of breath, The percentage with shortness of breath is (30/97) = 30.9%
20 of those that worked in other areas of the plant surveyed have only 1 person that reported shortness of breath. Percentage of those with shortness of breath = (1/20) = 5%
Now, taking each of the statements one at a time, we investigate whether they are great conclusions for this survey.
a) Since only 117 of the 135 workers in the plant participated in the survey, we must use caution when drawing conclusions.
Although, the 117 out of 135 workers that responded represent a a very large percentage of the 135 workers and this should make the findings for this 117 workers general for the total 135 workers, we need to exercise caution, especially if the 18 workers who did not respond to the survey are workers from other parts of the plant apart from the production area, and a lot of them possibly could have shortness of breath too, this greatly brings bias onto the entire survey.
But if the 97 workers from the production area and the 20 workers from the other parts of the plant who responded to the survey are randomly scattered through their respective groups and represent a high percentage of their respective groups, no need for caution then, as our results will be representative of all the workers.
b) Exposure to the chemicals in butter-flavoring is associated with a greater incidence of lung problems, such as shortness of breath.
Since the percentage of those who work in the production area who experience shortness of breath (30.9%) is way more than the percentage of those who work on other parts of the plant who experience shortness of breath (5%), we can say that 'Exposure to the chemicals in butter-flavoring is associated with a greater incidence of lung problems, such as shortness of breath' as only those in the production area inhale the chemical and those who work in other parts of the plant do not inhale these chemicals.
c) The chemicals in the butter-flavorings are causing shortness of breath because a much larger percentage of workers in the production area have shortness of breath.
Although, the percentage of those who work in the production area who experience shortness of breath (30.9%) is way more than the percentage of those who work on other parts of the plant who experience shortness of breath (5%), the survey doesn't totally show that it is the chemical being inhaled that is responsible for the respiratory issues.
d) Workers exposed to the chemicals in the butter-flavoring have a higher risk of developing respiratory problems such as shortness of breath.
Since the percentage of those who work in the production area who experience shortness of breath (30.9%) is way more than the percentage of those who work on other parts of the plant who experience shortness of breath (5%), we can say that Workers who work in the production area, exposed to the chemicals in the butter-flavoring have a higher risk of developing respiratory problems such as shortness of breath.
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