invest_3ed.pdf

# Discussion in the previous investigation the

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Discussion: In the previous investigation, the researchers literally took two different random samples from two different groups of teens. In this study, the data arose from one sample and each child in the sample was classified according to two variables: lighting condition and eye condition . A natural research question h ere might be “Does use of night lights and room lights increase the rate of near- sightedness in children?” In such a situation, we can instead phrase our hypotheses in terms of the association between the two variables: H 0 : There is no association between lighting condition and eye condition H a : There is an association between lighting condition and eye condition We can also state these hypotheses in terms of underlying population probabilities:

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Chance/Rossman, 2015 ISCAM III Investigation 3.2 197 H 0 : S light S darkness = 0 vs. H a : S light S darkness > 0 where i S represents the probability of a near-sighted child in population i. (c) Briefly discuss how you could modify the simulation procedure used in Investigation 3.1 to reflect the changes in the study design. It turns out, it will be valid to use the same inferential analysis procedures here as in Investigation 3.1 as long as the samples (e.g., room light, darkness) can be considered independent of each other. One counter example would be if the observational units had been paired in some way (e.g., brothers and sisters). But if we don’t believe the responses of particular children in lit rooms in this study in any way relate to the responses of particular children in the dark rooms, we consider the samples independent , even though they weren’t literally sampled separately, and use the same Central Limit Theorem to specify a normal distribution as a model of the sampling distribution of the difference in the two sample proportions. (d) Use technology to perform a two-sample z -test to compare the proportion with near sightedness between these two groups. Report the test statistic and p-value. Also report and interpret a 95% confidence interval from these data. (e) Because the p-value is so small, would you be willing to conclude that the use of lights causes an increase in the probability of near-sightedness in children? Explain. If not, suggest a possible alternative explanation for the significantly higher likelihood of near sightedness for children with lighting in their rooms. Discussion: When we find a highly significant difference between two groups, although we can conclude a significant association between the explanatory and response variables, we are not always willing to draw a cause-and-effect conclusion between the two variables. Though many wanted to use this study as evidence that it was the lighting that caused the higher rate of near-sightedness, for all we know it could have been children with poorer vision that asked for more light to be used in their rooms.
Chance/Rossman, 2015 ISCAM III Investigation 3.2 198 Or there could even be a third variable that is related to the first two and could provide the real explanation for the observed association.

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