Question

Resuelva cada uno de los ejercicios de pruebas NO paramétricas:

1. La efectividad de la publicidad para dos productos rivales (Marcas X e Y) fueron comparadas. Se hizo una investigación de mercado en un centro comercial local, donde a los participantes se les muestra un aviso publicitario de entre dos productos rivales de marcas de café, los cuales ellos evaluarán en una escala del 1 (definitivamente NO compraré el producto) al 10 (definitivamente SI compraré el producto). A la mitad de los participantes se les mostró el aviso publicitario de un producto mientras que a la otra mitad el del otro producto. Los datos obtenidos son los siguientes:

Brand X			Brand Y
Participant	Rating		Participant	Rating
1	3		1	9
2	4		2	7
3	2		3	5
4	6		4	10
5	2		5	6
6	5		6	8

Aplique una prueba de hipótesis para determinar si ambas marcas tienen la misma aceptación. En caso de no ser así indique que marca es más aceptada. Arroje conclusiones. Calcule el estadístico de prueba. Grafique (Graph) la región de rechazo. Calcule el valor p de la prueba (p-value).

English

Solve each of the non-parametric test exercises:

1. The effectiveness of advertising for two rival products (Trademarks X and Y) were compared. A market research was conducted at a local shopping center, where participants are shown an advertisement from two rival coffee brand products, which they will evaluate on a scale of 1 (I will definitely NOT buy the product) at 10 (I will definitely buy the product). Half of the participants were shown the advertising of one product while the other half of the other product. The data obtained are the following:

use data above

Apply a hypothesis test to determine if both brands have the same acceptance. If not, indicate which brand is more accepted. Throw conclusions. Calculate the test statistic. Graph (Graph) the rejection region. Calculate the p-value of the test (p-value).

Answer 1

t-Test: Two-Sample Assuming Unequal Variances
	X	Y
Mean	3.666666667	7.5
Variance	2.666666667	3.5
Observations	6	6
Hypothesized Mean Difference	0
df	10
t Stat	-3.781176708
P(T<=t) two-tail	0.003595014
t Critical two-tail	2.228138852

Let the mean ratings of X and Y are

Ho :

H1 :

Since p-value = 0.003595014 < 0.05 i.e Ho is rejected and hence both are not accepted and since mean of Y is high it can be said that Y is more accepted.

Test Statistic:

When n < 30 and not normally distributed, population variance is not known then,

t = [ (x₁ - x₂) - d ] / SE

Where,

DF = (s₁²/n₁ + s₂²/n₂)² / { [ (s₁² / n₁)² / (n₁ - 1) ] + [ (s₂² / n₂)² / (n₂ - 1) ] }

SE = sqrt[ (s₁²/n₁) + (s₂²/n₂) ]

d =

s1 = std. deviation of sample 1

s2 = std. deviation of sample 2