Question

Resuelva cada uno de los ejercicios de pruebas NO paramétricas:

Se han seleccionado aleatoriamente una muestra de 82 estudiantes de Instituto y otra con 46

estudiantes de centros privados y se ha considerado la nota en Educación Física para cada uno

de ellos. Los datos obtenidos vienen resumidos en la siguiente tabla de contingencia.

	Insuf	Suf o bien	notable	sobresaliente	total
Centro Privado (private center)	7	14	17	9	47
Instituto Institute	30	32	17	3	82
	37	46	34	12	129

1. Se desea contrastar la hipótesis de que la distribución de notas en Educación física es independiente del

             tipo de centro de Enseñanza

English 

sample of 82 Institute students was randomly selected and another with 46

students from private schools and the note in Physical Education has been considered for each

from them. The data obtained are summarized in the following contingency table.

Use the above table

We wish to contrast the hypothesis that the distribution of grades in Physical Education is independent of the type of teaching center

Answer 1

(Note: in the question, under column - 'remarkable', total is 34 not 3.4)

Null Hypothesis(H0):

The distribution of grades in Physical Education is independent of the type of teaching center.

Alternative Hypothesis(H1):

The distribution of grades in Physical Education is not independent of the type of teaching center.

Test statistic(​​​​​​):

Overall total, N =129

Expected value, E =Row total*Column total/N

Example:

For O =7, E =47*37/129 =13.4806

For O =30, E =82*37/129 =23.5194

Observed: O	Expected: E	(O-E)2/E
7	13.4806	3.1155
30	23.5194	1.7857
14	16.7597	0.4544
32	29.2403	0.2605
17	12.3876	1.7174
17	21.6124	0.9844
9	4.3721	4.8987
3	7.6279	2.8078
Total		16.0244

=16.0244

Critical value(_crit):

Number of rows, r =2

Number of columns, c =4

Degrees of freedom, df =(r-1)(c-1) =(2-1)(4-1) =3

Let the significance level, ​​​​​​

The critical value of Chi-squared value at 3 degrees of freedom and 0.05 significance level is _crit =7.815

Conclusion:

Since the test statistic of 16.0244 is greater than the critical value of 7.815 (_crit), we reject the null hypothesis(H0) at 0.05 significance level.

Thus, there is a statistically significant evidence to claim that the distribution of grades in Physical Education is not independent of the type of teaching center.