Question

A statistics teacher claims that, on average, 20% of her students get a grade of A, 35% get a B, 25% get a C, 10% get a D, and 10% get an F. The grades of a random sample of 100 are shown below. Use a = 0.05 to test the claim that the grades follow the distribution claimed by the teacher.   

Grade                # of Students

A                      29

B                      42

C                      20

D                        5

F                         4

  

Answer 1

null hypothesis:  Ho:grades follow the distribution claimed by the teacher.

alternate hypothesis:Ha: Not all grades follows the distribution claimed by the teacher.

degree of freedom =categories-1=5-1=4

for 4 df and 0.05 level rejection region >9.488

applying chi square goodness of fit :

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
A	0.200	29.000	20.000		4.050
B	0.350	42.000	35.000		1.400
C	0.250	20.000	25.000		1.000
D	0.100	5.000	10.000		2.500
E	0.100	4.000	10.000		3.600
total	1.000	100	100		12.550

as test statistic 12.550 is in critical region we reject null hypothesis

we have sufficient evidence at 0.05 level to reject  the claim that the grades follow the distribution claimed by the teacher.