It is hypothesized that interacting with bluelight emitting devices within the hour before sleep is associated with less sleep. Suppose you want to test this so you set up an experiment where the participants are randomized to either using a light emitting e-reader an hour before sleeping or reading a paper book an hour before sleeping. After recording the total hours of sleep for one week, you observe an an average 56 hours per week for the paper book reading group average 42 hours per week for the e-reading group. There were 12 participants in each group. (a) What is the parameter of interest in this study? (b) What assumptions, if any, do you have to make about the parameter in (a) for the expected value of the difference to be 14 hours? (c) The standard deviation for the paper book and e-reader groups were 7.9 and 4.3
hours respectively. What is the standard error of the difference between the average hours of sleep per week between the two groups? (d) IfXˉ book =56 andXˉbook =42, what is the distribution of
Xˉbook − Xˉ eread ? (e) What is the probability that the difference in average sleep per week between those who read a paper book and those who read an e-reader is less than 7 hours? (f) Construct a
90%
confidence interval for the difference in average hours of sleep per week between those who read paper books and those who read e-readers before sleeping, and provide a conclusion in context. Be sure to use the confidence interval information to conclude about the original hypothesis.
