Acity wants to show that the mean number of public transportation users per day is more than 5,575. identify the null hypothesis, h0, and the alternative hypothesis, ha, in terms of the parameter μ.

Step-by-step explanation:

Given : A city wants to show that the mean number of public transportation users per day is more than 5,575.

To Find : Identify the null hypothesis, , and the alternative hypothesis, , in terms of the parameter μ.

Solution:

Claim :  A city wants to show that the mean number of public transportation users per day is more than 5,575.

So, Null hypothesis :

Alternate hypothesis :

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!