The National Assessment of Educational Progress (NAEP) includes a mathematics test for eigth-grade students. Scores on the test range from 0 to 500. Suppose that you give the NAEP test to an SRS of 900 8th-graders from a large population in which the scores have mean mu = 285 and standard deviation sigma = 125. The mean x-bar will vary if you take repeated samples. Suppose that we took an SRS of 1600 8th-graders and found x-bar =288. Compared with an SRS of 900 8th-graders, the margin of error for a 95% confidence interval for mu is

Exercise: counting committees 0.0/2.0 puntos (calificable) we start with a pool of n people. a chaired committee consists of k≥1 members, out of whom one member is designated as the chairperson. the expression k(nk) can be interpreted as the number of possible chaired committees with k members. this is because we have (nk) choices for the k members, and once the members are chosen, there are then k choices for the chairperson. thus, c=∑k=1nk(nk) is the total number of possible chaired committees of any size. find the value of c (as a function of n ) by thinking about a different way of forming a chaired committee: first choose the chairperson, then choose the other members of the committee. the answer is of the form c=(α+nβ)2γn+δ. what are the values of α , β , γ , and δ ?