4. An experimenter was interested in studying the effects of sleep deprivation on the ability to detect moving objects on a radar screen. A total of 20 students were available for the study. The rst ve randomly selected subjects were assigned to Treatment Group 1 (4 hours without sleep), the next ve randomly selected subjects were assigned to Treatment Group 2 (12 hours without sleep), the next ve randomly selected subjects were assigned to Treatment Group 3 (20 hours without sleep), and the remaining ve subjects were assigned to Treatment Group 4 (28 hours without sleep). After being deprived of sleep, each subject was given a test and the number of times they failed to spot a moving object during the set test period was recorded. The results are given in the following table: 4 Hours 12 Hours 20 Hours 28 Hours 36 38 46 76 21 45 74 66 20 46 67 4 62 26 22 61 44 21 4O 59 61 (a) Is this study an experiment of an observational study? (b) Give a name for the explanatory variable in this study. (c) Give a name for the response variable in this study. (d) The study stated that the 20 subjects were randomly assigned to one of four treatment groups. Using your calculator (with a seed value of 14), perform the randomization. Report the labels of the subjects assigned to each of the four groups. (e) State the appropriate null and alternative hypotheses for assessing whether the mean I rrq r .u .- number of failures is the same for the four sleep-deprivation conditions. (f) Create 95% condence intervals for the population means for each level of the experiment (e.g. 4 hours, 12 hours, etc.) and draw a spatially representative graph as l demonstrate in the ANOVA video lecture linked above. (g) Explain what the statistical analysis reveals about the effects of sleep deprivation on the subjects' ability to detect objects while sleep deprived. 5. A nutritional expert randomly assigns 18 bicyclers to three groups. Group B is given a vitamin supplement, and Group C is given a diet of health foods. Group A is instructed to eat as they normally do.l After a set time period on the prescribed diets, the expert subsequently records the number of minutes it takes each person to ride six miles. The data are provided in the following table: Group A Group B Group C 19 16 18 12 16 14 18 15 14 14 17 13 State the appropriate null and alternative hypothesis and conduct a oneway analysis of variance of this study. If Hois rejected, estimate the population mean for each group using a 95% condence interval. Draw a graph representing all three condence intervals together as in the video lecture for ANOVA