supplier evaluation using population proportion tests hypothesis

Case Study:

A manufacturer of walk-behind push mowers receives refurbished small engines from two new suppliers, A and B. It is not uncommon that some of the refurbished engines need to be lightly serviced before they can be fitted into mowers. The mower manufacturer recently received 100 engines from each supplier. In the shipment from A, 13 needed further service. In the shipment from B, 10 needed further service. Test, at the 10% level of significance, whether the data provide sufficient evidence to conclude that there exists a difference in the proportions of engines from the two suppliers needing service.

Solutions:

#Input:

sample_A_size = 100

sample_A_prop = 0.13

sample_B_size = 100

sample_B_prop = 0.10

alfa = 0.10

#STEP 1: Hypo 

#H0 = Pa - Pb = D0 = 0: no difference in the test population

#Ha = Pb != Pb : there is a differenc in supplier products 

#STEP 2 & 3: statistic test

z_statistic = (sample_A_prop - sample_B_prop - 0 )/ 

                  sqrt((sample_A_prop*(1- sample_A_prop) + sample_B_prop*(1-sample_B_prop))/ sample_A_size )

#STEP 4 & 5  Rejection Region:

z_value = - qnorm(.05, 

      mean = 0, 

      sd = 1)

c(between(z_statistic, z_value, Inf), 

  between(z_statistic, -Inf,  - z_value))

#[1] FALSE FALSE

p_value = pnorm(z_statistic, 

                mean = 0, 

                sd = 1)

#[1] 0.747

Conclusion:

The test statistic does not fall in the rejection region. The decision is not to reject H0. In the context of the problem our conclusion is: The data provide sufficient evidence, at the 10% level of significance, to conclude that there exists no difference in the proportions of engines from the two suppliers needing service.

using p-value approach: since the p-value < alfa or the confidence level the decision is the same as above