Chi Square Distribution

Imagine we want to know how popular a new method of teaching English by the native Americans teachers from Boston and Michigan, USA is accepted by the students in this UTHM and three other colleges as compared to the present method where Dr S a Kelantanese prince teaching English in PR and the surrounding places.

We get this table. 2 x 4 Contingency table – 2 rows and 4 columns

UTHM / KKTM / KPMara / PJB / total
68 / 75 / 57 / 79 / 279
32 / 45 / 33 / 31 / 141
100 / 120 / 90 / 110 / 420

Now using symbols

Puthm = proportion in uthm who prefer present method

Pppktm= proportion in PPKTM who prefer present method of teaching and learning

Pptmara= proportion in polytechnic mara who prefer present style

Ppjb = proportion in PJB who prefer the present style

Hypothese :

HO : Puthm=Pppktm=Pptmara=Ppjb -----à null hypothesis

H1: Puthm, Pppktm,Pptmara,Ppjb are not all equal -à alternative hypothesis

If the null hypothesis is true, we can combne the data from the 4 samples and then estimate the proportion of the total student population that prefers the present style of teaching and learning.

Combined proportion who prefer present method assuming the null hypothesis of no difference is true

= ? = 0.6643

Thus if 0.6643 estimates the proportion population expected to prefer this old style of teachning and learning then 0.3357 is the proportion who dislikes the old style and of course like the new style introduced into the education establishments.

We get another table below

Expected to prefer the two review methods

UTHM / KKTM / KPMara / PJB
Total Number sampled estimated to prefer present method / 100* 0.6643= 66.43 / 120*0.6643=79.72 / 90*0.6643= 59.79 / 110*0.6643= 73.07
Total Number sampled estimated to prefer the newest method (employing American teachers in english lessons as a whole) / 100*0.3357= 33.57 / 120* / 90* / 110
UTHM / KKTM / KPMara / PJB
Actual frequency OLD METHOD
Expected (theoretical ) frequency / 68
66.43 / 75
79.72 / 57
59.79 / 79
73.07
Frequency preferring new method / actual number
And
expected Number who prefer new method / 32
33.57 / 45
40.28 / 33
30.21 / 31
36.93

The chi square statistics

= 2.7638

Determining the degrees of freedom

(number of rows -1) ( number of columns -1) = 3 degrees of freedom

Check with the table of chi squared

Under10% column on the right of the 1 tailed test

You get 6.251

Thus you see this is not inside the non critical zone.

------X------|------

2.764 6.251

Accept ------| REJECT Ho

Conclusion:

Within the acceptance region.

Therefore you accept the null hypothesis. There is no difference between attitude of students preferring the old malay teachers teaching English at the 4 institutions of higher learning around P.R. Johor and the American teachers teaching English like the students in Boston and Michigan, USA.