I'm having difficulty in doing number 4, I know it's paired data but not sure how to do the rest. Could someone please show me and I will try the next question. My lecturer haven't gone through the hypothesis testing topic yet but I want to get this out of the way so I can do

other subjects. Thank you

Question 4 [11 Marks] A researcher wants to know whether lack of sleep affects the scores soldiers achieve in a test of shooting ability. Nineteen volunteers undertake the test after a normal night of sleep. One month later, each volunteer retakes the test after a 24-hour period without sleep. The scores of each volunteer on the two tests are shown below. Volunteer 2 3 4 5 6 7 8 9 10 Test score after sleep 33 26 23 16 25 21 17 30 22 Test score without sleep 29 13 20 13 19 18 16 14 22 24 Volunteer 11 12 13 14 15 16 17 18 19 Test score after sleep 23 19 22 17 16 22 35 24 15 Test score without sleep 13 23 14 9 13 23 22 18 10 a) Is this paired or unpaired data? b) Calculate the summary statistics relevant to this problem. Page 2 of 4 MONASH University Science Semester 1, 2021 c) Compute a 95% confidence interval for the mean change in score between the two tests. Show all your working. d) Based on that confidence interval, is there sufficient evidence to conclude that scores are lower after a sleepless night? In your answer, comment on the relationship between confidence intervals and 2-sided hypothesis tests. e) The researcher wants to estimate the mean change in test score to an accuracy of +1 with 95% confidence. How many volunteers would be needed to achieve this? f) Use a nonparametric hypothesis test to further investigate whether there is a difference between test scores with and without sleep. g) Is a parametric or non-parametric test more appropriate here? Question 5 [12 Marks]