The grades in a statistics course for a particular semester were as follows: Grade ABCDF f 14 18 32 20 16
Test the hypothesis, at the 0.05 level of significance, that the distribution of grades is uniform. (Test that each grade is equally likely) Round your solutions to 3 decimal places where necessary.
Test Statistic =
Critical Value =

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

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11-1 > 1-1+a

-12 > a

the surface area is 124cm²

step-by-step explanation:

length: 4cm

width: 9cm

height:   2cm