Question

Resuelva cada uno de los ejercicios de pruebas NO paramétricas:

Una agencia publicitaria está investigando a qué tipo de avisos le prestan más atención los

adolescentes. Se observan a 11 niños, a 6 se les muestra avisos sobre comida y a los 5 restantes

se les muestra avisos sobre bebidas. Todos los avisos tienen duración similar. Se registra el

tiempo de atención (en segundos) de los 11 niños.

Los datos se resumen a continuación:

Tipo aviso/ Notice type	B	C	B	B	B	B	C	C	C	C	C
Datos Ordenados/ Ordered Data	23	25	28	30	35	38	41	42	45	47	50

1. Aplique una prueba NO paramétrica para determinar si existen diferencias estadísticamente significativas entre ambos grupos. De haberlas, diga cual es el grupo de avisos al que los niños le prestan mayor atención. Muestre todo el procedimiento. Calcule el estadístico, y arroje conclusiones.

English

An advertising agency is investigating what kind of ads pay more attention to
teenagers. 11 children are observed, 6 are shown notices about food and the remaining 5
They are shown warnings about drinks. All notices have a similar duration. The registration is recorded attention time (in seconds) of the 11 children.

The data is summarized above:

Apply a non-parametric test to determine if there are statistically significant differences between both groups. If there are, tell which is the group of notices to which the children pay more attention. Show the whole procedure. Calculate the statistic, and draw conclusions.

Answer 1

Mann Whitney U test is a appropriate non-parametric test used to determine if there are statistically significant differences between two groups.

Given the dataset showing attention time (in seconds) of the two group of children.

Group 1 (Notices about food)	Group 2 (Warnings about drinks)
25	23
41	28
42	30
45	35
47	38
50

HYPOTHESIS:

The hypothesis for the Mann Whitney U test is given by,

(That is, there is no significant difference in attention times between the group that notices food and the group that are shown warning about drinks.)

(That is, there is significant difference in attention times between the group that notices food and the group that are shown warning about drinks.)

Now rank the two groups together.

Group 1 (Notices about food)		Group 2 (Warnings about drinks)
25	2	23	1
41	7	28	3
42	8	30	4
45	9	35	5
47	10	38	6
50	11

Sample size of group 1

Sample size of group 2

Since the sample sizes are unequal, we will check for the condition

Thus the condition is not satisfied.

LEVEL OF SIGNIFICANCE:

TEST STATISTIC:

The test statistic is given by,

where

and

CALCULATION:

  

  

  

  

Thus

  

Mann Whitney U test table:

CRITICAL VALUE:

From the Mann Whitney U test table, the two tailed value with and is .

INFERENCE:

Since the calculated test statistic value (4) is greater than the critical value (3), we reject null hypothesis and conclude that there is statistically significant difference in attention times between the group that notices food and the group that are shown warning about drinks.

Now to find the group to which the children pay more attention, we check the average ranks. Since , the median attention time for the group of children that notices about food is greater than the median attention time for the group of children that are shown warnings about drinks. In other words, the children pay more attention to the group that notices about food.