In Exploration 8.2B, we will look at a study that was done to determine if there is an association between the amount of light in infants€™ bedrooms at night (darkness, night light, room light) and whether or not the child was nearsighted when they were older. A summary of the data from that study is shown in the following table. We are interested in determining if there is an association between the type of light in the room and whether or not the child is nearsighted.

a. What is the explanatory variable in this study? Is it categorical or quantitative?
b. What is the response variable in this study? Is it categorical or quantitative?
c. Write out the null and alternative hypotheses for this study.
d. Compute the observed proportions of children that are nearsighted for each lighting condition.
e. Compute the MAD statistic.
f. A null distribution was generated for this data set and is shown. Based on this distribution along with the MAD statistic, what can you say about the value of the p-value?

g. What is your conclusion based on this p-value?

Night light Room Darkness light Total 18 41 137 78 78 Nearsighted Normal vision 154 342 154 34 75 Total 172 232 479 Mean = 0.045 1000 SD = 0.024 800 600 400 200 0.04 0.08 0.12 0.16 Shuffled MADS Count