In: Statistics and Probability
Education is the most important thing in everyone's life , It is vital to gain knowledge and expertise in their area of interest to get a good job earning them and their families a living .
For the poorer community, the education becomes more vital because they can't depend on their families for living for a longer time . Studies show that the families with children having proper education became economically stable than the those families with children without education .
The following data gives us the salaries (in 100 dollars)of 15 families of two groups (one with properly educated and other without proper education)
Educated | 68 | 76 | 78 | 70 | 81 | 77 | 72 | 75 |
---|---|---|---|---|---|---|---|---|
Uneducated | 34 | 39 | 38 | 36 | 35 | 41 | 40 |
Since we are using two independent groups , we use two sample independent t test to compare the means of 2 groups and we get p value less than .05 which implies that educated earn more than uneducated
So education is vital for poor children
From the school you are studying , get the students along with their last examination marks
From the non-tution group of children select a sample of 5 children and the same from the tution group and their last exam scores are given below
Tution students |
87 | 84 | 91 | 97 | 94 |
---|---|---|---|---|---|
Non-Tution students |
68 | 45 | 39 | 58 | 51 |
On seeing the table itself we can identify tution students do well than the non tution students which is evident from the fact the mean of the two groups are 90.6 and 52.2 and the variance among the group is low for rich (27.3) when compared to the rich group (127.7).
Now the class teacher wants to help the poorly studying students to improve their grades and she believes that those students don't spend more time at home on studies .
So she asks the students to come to her home for tutions and this continues for 3 months .
After 3 months she again collects the score of the children sampled before and it is as follows
Tution students | 90 | 81 | 86 | 91 | 95 |
---|---|---|---|---|---|
Non Tution students | 78 | 76 | 80 | 79 | 74 |
Here also the mean score of tution is high when compared to the non tutioner but the mean score for non tutioner has increased to 77.4 and the variation is just 5.8 compared to 28.3 of the already tution going group which implies that the tution makes the weak students study well and the coaching is reaching all because the variation is low
We can use paired sample t test to check whether the coaching impacts on education at the given level of significance .
If the teacher continues her tutions the weak students can score more