Homework 1 for Statistics 101-106 (Fall 98)

Due: Thursday 17 September

(0.1) Compare the rankings that would be obtained from the Yale grades by combining the final exam score and the classwork score in three different ways: (i) add the two scores together; (ii) add the two standardized scores together; (iii) adjust scores by rescaling to make the interquartile ranges the same before adding.

Which method of combination do you consider the fairest, in the sense of coming closest to the stated purpose of giving the final exam and the homeworks+midterm equal weight in calculating the grade for the course? Explain. Suggestion: Consider some students who get very different rankings under at least two of the methods.

(0.2) The Irish wind speed data are given in knots (1 knot is approximately 1.15 miles per hour). The Beaufort scale defines a strong breeze as a wind speed between 25 and 31 miles per hour. (i) On what fraction of the days did the average wind speed at Malin Head (MAL) qualify as a strong breeze? (ii) Calculate the theoretical proportion of strong breezy days (based on the average wind speed) at Malin Head if the square roots of average wind speeds followed a normal distribution with the same mean and standard deviation as (the square roots of) the observed data.

Each Section will assign extra problems.