7. A population has a mean of 85 and SD of 9. If many samples of size

7. A population has a mean of 85 and SD of 9. If many samples of size

7. A population has a mean of 85 and SD of 9. If many samples of size n = 100 are randomly drawn from the population, approximately what proportion of the sample means fall between 84 and 86? Explain your answer and show work8. It has been extensively demonstrated that adequate night sleep is crucial for cognitive performance. To investigate whether first year USC students are getting adequate sleep the night before a final exam, 81 randomly selected first year USC students were asked to record their number of hours of sleep the night before their final exams. The mean number of hours of sleep among the 81 students was 6.2 with an SD of 1.5 hours. a. Identify the population, sample, and parameter of interest in this study.b. Construct a 95% CI for the mean number of hours first year USC students sleep the night before an exam. Explain the meaning of this CI (you are expected to explain what this confidence interval says about the parameter of interest)c. Now construct a 99% CI for the mean number of hours first year USC students sleep the night before an exam. Explain the meaning of this CI and contrast with the 95% CI in part b. d. Suppose the 81 students represent a subset of a larger pool of 100 students randomly selected for the study. The 81 students provided the investigators with their number of hours of sleep, while the remaining 19 students did not respond when contacted by the investigators. If the 19 non-responders were more likely to sleep more hours before an exam than a typical first year USC student, how would this affect the estimate and CI for the mean number of hours first year USC students sleep the night before an exam?