Question

[Q#1] (7pts) A recent survey polled 120 men and 80 women to determine their level of education. The results are presented in the table. We wish to test whether the education level is Observed High School Bachelor's Graduate independent of the gender. Compute the expected Frequency Diploma Degree Degree frequencies and the value of the Chi-square test statistic. Men 30 40 50 Women 15 45 20

Answer 1

Given :

A recent survey polled 120 men and 80 women to determine their level of education. The results are presented in the table.

Observed frequency	High school Diploma	Bachelor's Degree	Graduate Degree	Total
Men	30	40	50	120
Women	15	45	20	80
Total	45	85	70	200

Expected frequency = (row sum*column sum) / Grand sum

E1 = 120*45/200 = 27

E2 = 120*85/200 = 51

E3 = 120*70/200 = 42

E4 = 80*45/200 =18

E5 = 80*85/200 = 34

E6 = 80*70/200 = 28

Chi square goodness of fit test :

Category	Observed frequency (Oi)	Expected frequency (Ei)	(Oi-Ei)^2/Ei
1	30	27	0.3333
2	40	51	2.3725
3	50	42	1.5238
4	15	18	0.5
5	45	34	3.5588
6	20	28	2.2857
Total	200	200	10.5741

The value of Chi square test statistic is $\chi^2$ = 10.574...( rounded to 3 decimal places)