Investigation 11: Night-lights and near-sightedness (due Thur, Feb 23)

You may work with one other person on this assignment, handing in one report with both names.  Word-processed reports are preferred to hand-written ones.  Please copy/paste relevant, well-labeled Minitab output into a Word file as appropriate.

Myopia, or near-sightedness, typically develops during childhood years. Recent studies have explored whether there is an association between development of myopia and the use of night-lights with infants. One study interviewed parents of 479 children who were seen as outpatients in a university pediatric ophthalmology clinic. One of the questions asked whether the child slept in room light, darkness, or with a night light before age 2. Based on the child’s most recent eye examination, the children were also separated into three groups: near-sighted, far-sighted, or normal refraction. The results are presented in the following two-way table:

	Darkness	Night light	Room light	Total
Near-sighted	18	78	41	137
Normal refraction	114	115	22	251
Far-sighted	40	39	12	91
Total	172	232	75	479

(For two examples of how to read the table, the upper-left cell indicates that 18 children slept in darkness and were near-sighted. The lower-right cell (excluding the “total” row and column) reveals that 12 children slept in room light and were far-sighted.)

a) Identify the observational units in this study.

b) Identify the explanatory variable and the response variable in this study. Is it categorical or quantitative?

c) Is this an experiment or an observational study? Explain how you can tell.

d) For each lighting condition, determine what proportion of the children who slept in that condition ended up with near-sightedness.

e) Conduct a chi-square test of whether these data provide strong evidence of an association between lighting condition and eyesight condition. Report the hypotheses, test statistic, and P-value. Also summarize your conclusion.

f) Is it valid to conclude that sleeping in a lit room, or with a night light, causes an increase in a child’s risk of near-sightedness?  If so, explain why. If not, identify a confounding variable that offers an alternative explanation for what the data in the table reveal, and explain why it is confounding.