STAT464 Homework #2due Monday, 9/91. (adapted from Higgins, Ex1.1 ) The data are given in the file “exam scores.txt”. Supposethe exam was given in the semester after the course content was revised, and the previousmedian exam score was 75.5. We would like to know whether or not the median score hasincreased. Answer the question by applying the sign test. The data can be read into R withthe commandscores = scan(’exam scores.dat’,skip=1)2. Consider again the exam score data above.(a) Perform the usual t-test of H0 : µ = 75.5 versus Ha : µ > 75.5. Report the test statisticand p-value, and state your conclusion in terms of the problem.(b) Comment on any similarities and differences between this test and the Sign test fromProblem 1.3. (adapted from Higgins, Ex1.3 ) The data, given in the file “rainfall.txt”, are yearly rainfalltotals in Scranton, Pa., for the years 1951–1984.(a) Find order statistics X(a) and X(b)such that (X(a), X(b)) is an approximate 95% confi-dence interval for the population median θ.5. Use the binomial distribution. Report thenumeric values of your interval here as well.(b) Use the normal distribution (with 1/2-unit continuity correction) to find the approximate
STAT464作业代做confidence level of your interval in part (a) above.(c) Find an approximate 95% confidence interval for the 75th percentile (the third quartile).You may use either the binomial or the normal distribution (with 1/2-unit correction).(d) The confidence interval procedure assumes that the observations are independent andidentically distributed. Do you think this is a reasonable assumption for the rainfalldata? If not, what could cause this assumption to be invalid?
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