STAT 205 Homework 7 (Due: 5:00 Pm, Tuesday, March 7, 2017)

STAT 205 Homework 7 (Due: 5:00 pm, Tuesday, March 7, 2017) Instructor: Shiwen Total Points: 70

Submission instruction: Answer all the questions individually in one file. (You can either write your answers on A4 papers and scan to the computer, or type directly in Microsoft Word.) Show all the calculation steps and R outputs. Put your name on the top line and submit the completed word file on the blackboard.sc.edu Assignments section before the deadline. (EMAIL SUBMISSION WILL NOT BE ACCEPTED)

1. In the context of the Exercise 6.3.3 in page 191, construct 90%, 95% and 99% confidence interval for the population mean and write a proper interpretation for the 95% confidence interval. Use R. (10) 2. Textbook page 192, Exercise 6.3.8. (10) 3. Textbook page 192, Exercise 6.3.9. (10) 4. Six healthy 3-year-old female Suffolk sheep were injected with the antibiotic Gentamicin. Their blood serum concentrations of Gentamicin were measured. Calculated by the data, we have sample mean 28.7, and we know that the population standard deviation is 4.6. Construct a 95% confidence interval for the population mean by hand. (10) 5. In the context of the Exercise 6.7.13 in page 217. Use R to construct the 95% confidence interval for the difference in mean, and write a proper interpretation for the interval. In addition, use R to construct the 95% confidence interval for the ratio of two population variances . (Hint: before constructing the confidence interval, do not forget to check the normality for both red and green data.) (30)