The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. she obtained the data on percentage of students passing the proficiency test (% passing), mean teacher salary in thousands of dollars (salaries), and instructional spending per pupil in thousands of dollars (spending) of 47 schools in the state. following is the multiple regression output with y = % passing as the dependent variable, x1 = salaries and x2 = spending: which of the following is the correct null hypothesis to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables? a) h1: =b3=0

b) h1: =b1=0

c) h1: =b2=0

d) h1: =b0=0

Suppose we have a set of small wooden blocks showing the 26 letters of the english alphabet, one letter per block. (think of scrabble tiles.) our set includes 10 copies of each letter. we place them into a bag and draw out one block at a time. (a) if we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) now suppose we just toss our chosen blocks into a pile, and whenever we draw a letter we already have, we put it back in the bag and draw again. how many different piles of 5 blocks could result? possible? piles will contain at least one repeated letter? (c) if we draw out 5 blocks wit hout looking at them, how many different piles are (d) if we draw out 5 blocks without looking at them, how many of the possible 2. (4) consider the following formula. 12 give two different proofs, one using the factorial formulas and the other combina torial.

Alarger number is double the sum of a smaller number. the larger number is 2 less than 3 times the smaller number. if y represents the larger number and x represents the smaller number, which equations model the situation

The investigating team suspected that there were differences in the cost of repairing cars in workshop i and workshop ii. the investigating team suspected that the costs raised by workshop i were greater than workshop ii. for that they tested the repair of 15 cars in each workshop to see the cost of repairs.the decision of the right hypothesis to prove the suspicion above is a. h0 : μ1- μ2­ = 0; ha : μ1- μ2­ ≠ 0 b. h0 : μ1- μ2 ≥ 0; ha : μ1- μ2 < 0 c. h0 : μd ≥ 0; ha : μd < 0 with μd = μ2- μ1 d. h0 : μd = 0; ha : μd ≠ 0 with μd = μ2- μ1 e. h0 : μ1- μ2 = 0; ha : μ1- μ2 ≥ 0