Question

A statistics professor posted the following grade distribution for her elementary statistics class: 8% A, 35% B, 40% C, 12% D, and 5% F. A sample of 100 elementary statistics grades at the end of last semester showed 12 As, 30Bs, 35Cs, 15 Ds, and 8 Fs. Test at the 5% significance level to determine whether the actual grades deviate significantly from the posted grade distribution guidelines. write the 5 step procedure.

Answer 1

Step 1:

H0: Null Hypothesis: The actual grades do not deviate significantly from the posted grade distribution guidelines.

HA:Alternative Hypothesis: The actual grades deviate significantly from the posted grade distribution guidelines. (Claim)

Step 2:

Test Statistic () is got as follows:

Observed (O)	Expected (E)	(O - E)2
12	100 X 0.08 = 8	2.000
30	100 X 0.35 = 35	0.714
35	100 X 0.40 =40	0.625
15	100 X 0.12 = 12	0.750
8	100 X 0.05 = 5	1.800
Total = =		5.889

Step 3:

= 0.05

df = 5 - 1 = 4

From Table, critical value of = 9.488

Rejection Region:

Reject H0 if > 9.488

Step 4:

Since calculated value of = 5.889 is less than critical value of = 9.488, the difference is not significant. Fail to reject null hypothesis.

Step 5:

The data do not support the claim that the actual grades deviate significantly from the posted grade distribution guidelines.