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STAT464 Homework #2

due Monday, 9/9

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% confi-

dence interval for the population median θ.5. Use the binomial distribution. Report the

numeric values of your interval here as well.

(b) Use the normal distribution (with 1/2-unit continuity correction) to find the approximate

confidence level of your interval in part (a) above.

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 and

identically distributed. Do you think this is a reasonable assumption for the rainfall

data? If not, what could cause this assumption to be invalid?