Question

(3 Marks) ON FIVELIS MARKS )A University bas been awarding its postgraduate students A, B, C and D in the ai 1:2 5:7 Io order to improve student's performance special tutorial classes have heen arranged by ac University, after which 800 students are graded as follows Grade No. of Students 78 192 308 By testing the hypothesis, check if theze is an improvement in postgraduate stulents' pertormance afler special tutorial classes 6 Marks)

Answer 1

Hypothesis
Ho : The distribution of the students after the special tutorial is the same mentioned by the university
H1 : The distribution of the students after the special tutorial is not the same mentioned by the university

We need to use a chi-square test to test this hypothesis.

The Observed and Expected distribution of grade as is shown below.

The observed distribution of the grades after the special tutorial as given in the question.

The expected distribution is obtained from the ratios by which the university gives the grades.

Therefore we have

1x + 2x + 5x + 7 x = 800
15x = 800
x = 53.33

Hence the expected distribution is
A = 1*53.33 = 53
B = 2*53.33 = 107
C = 5*53.33 = 267
D = 7*53.33 = 373

To find the chi stat we use the following

$\\Chi.stat = \sum \frac{(O-E)^2}{E}\\ Chi_stat = \frac{(78-53)^2}{53}+\frac{(192-107)^2}{107}+\frac{(222-267)^2}{267}+\frac{(308-373)^2}{373}=98.23\\$

df of freedom = (no.of row -1) (no of row - 1) = 4-1=3

Pvalue using the chi square table = 0.000000

Since the pvalue is less than 0.05, we reject the null hypothesis.
We conclude that the distribution of the students after the special tutorial is not the same mentioned by the university