For each of the following, state the null and alternative hypotheses, the type 1 and type ii errors associated with the hypotheses and the consequences of each error.

the decision to implement changes in the current math program at a junior high in bigcity will be based on a sample of students scores on a standardized math exam. if the average is less than the statewide average of 89 all math teachers will have to participate in a workshop to revise the curriculum.

expensive clothing inc. thinks it had a good year and wants to rewards it customers. in a typical year sales are $75 per customer. if a random sample of this years sales indicate a better than average year a $10 coupon will be given out for two weeks to each customer who spends atleast $75.

too many pets, a pet store, is concerned about its dogs. the store has enough supplies on hand to maintain an estimated in-store average of 10 dogs a day. the store wants to know whether its average dog population is actually 10 a day or some other number. if their original estimate is incorrect the store will have to invest in research to determine the actual average and decide how to accommodate the change.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

step-by-step explanation:

we can use this expression to calculate the energy gain as a particle moves with a field or the energy loss as it moves against it. (note that it is also used to define the electron-volt, a unit of energy equal to that gained by an electron as it falls through a pd of 1 v, i.e. w = 1 ev = 1.6 10-19 c 1 v = 1.6 10-19j).in fact this expression is really nothing more than the statement that potential is the potential energy per unit charge. in this case, v= w/qis simply stating that the change in potential energy(or work done) per unit charge is equal to the change in potential (or potential difference), v.student questions: uniform electric fields2electron beamcathode+5 kvanode0 v