Question

INSTRUCTION: MUST SHOW YOUR WORK TO RECEIVE CREDITS, especially the quantities you use to get answer. [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 15 Women 20 45

Answer 1

Answer:

If we calculate the total of each group we will have the following table:

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

Now if we see that out of 200 students 120 are men and 80 are women

so probabitliy value of men = 120/200 = 0.6

so probability value of women = 80/200 = 0.4

Based on this, we can calculate the expected value of men and women in each grade

	High school Diploma	Bachelor’s degree	Graduate Degree	Total
Men	27	51	42	120
Women	18	34	28	80
Total	45	85	70	200

Calculation:

For men in high school = total student in highschool * probabiltiy value for men = 45*0.6 = 27

For women in high school = total student in highschool * probabiltiy value for women = 45*0.4 = 18

same calculation we have applied of for other grade:

Now for chi square we can create the below table:

	High school Diploma	Bachelor’s degree	Graduate Degree	Total
Men	0.333333333333332	2.37254901960785	1.52380952380952	4.2296918767507
Women	0.5	3.55882352941176	2.28571428571429	6.34453781512605
Total	0.833333333333333	5.93137254901961	3.80952380952381	10.5742296918767

Calculation

= (observation -expected value)^2/expected value

for men in highschool = (30-27)^2/27 = 0.333

Same we have calculated squre of all the scenario

chi squre = sum of ((observation -expected value)^2/expected value)

chi square = 10.57423

Now if we look at the chi square table for (3-1)*(2-1) = 2 degree of freedom, p-value is 0.005057

As p -value is less than 0.01 so with 99% Ci, we can reject the null hypothesis and accept the alternate hypothesis.

So with 99% CI we can say that educational level is not independant of the gender