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1. (adapted from Higgins, Ex1.1 ) The data are given in the file “exam scores.txt”. Suppose
the exam was given in the semester after the course content was revised, and the previous
median exam score was 75.5. We would like to know whether or not the median score has
increased. Answer the question by applying the sign test. The data can be read into R with
the command scores = 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 statistic
and 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 from
Problem 1.
3. (adapted from Higgins, Ex1.3 ) The data, given in the file “rainfall.txt”, are yearly rainfall
totals 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% confidence interval for the population median θ.5. Use the binomial distribution. Report the
numeric values of your interval here as well.