An automobile manufacturer claims that its jeep has a 53.9 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 110 jeeps, they found a mean MPG of 53.7. Assume the standard deviation is known to be 1.8. A level of significance of 0.02 will be used.

Find the value of the test statistic.

Value of the test statistic,

Step-by-step explanation:

Null hypothesis,

Alternative hypothesis,

Sample mean,

Sample size, n = 110

Standard deviation,

Significance level,

The value of the test statistics is given by the formula:

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!

bn,mn,n.vn.

step-by-step explanation: