Answer:
Test Statistic = 10
Critical Value = 9.488
Step-by-step explanation:
Given :
Grade A _ B _ C _ D _ F
_____14 _ 18 _32_ 20_16
H0 : distribution of grade is uniform
H1 : Distribution of grade is not uniform
Using the Chisquare statistic :
χ² = (observed - Expected)² / Expected
The expected value :
(14+18+32+20+16) / 5 = 20
χ² = (14-20)^2 / 20 + (18-20)^2 / 20 + (32-20)^2 / 20 + (20-20)^2 / 20 + (16-20)^2 / 20
χ² statistic = 10
The χ² critical at df = (n - 1) = 5 - 1 = 4
χ² Critical(10, 4) = 9.488
Five items plus ten dollars
The trapezoid has two right triangles each with one side of length (13-9)2 = 4/2 = 2.
The other side of each right triangle is such that tan 60° = Heigth / 2
Then height = 2*tan60°.
The area of the trapezoid is height * (base 1 + base 2)/2
Then area = 2*tan (60°) * (13+9)/2 = 38.11
Area of triangle = (1/2)*b*h = (1/2)*7*10
= 7*5 = 35 squared cm
