Question

A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs? In an actual experiment, 100 consumers were asked to pick the design they preferred. The following data were obtained. Do the data appear to confirm the belief that one design is just as likely to be selected as another? Explain

design number of times preferred
1 5
2 15
3 30
4 40
5 10

Answer 1

we assume that one design is just as likely to be selected by a consumer as any other design

so the probability for all is same = 1/5

However , according to the actual experiment :

P(package 1 is selected ) = 5/100 = 1/20 = 0.05

P(package 2 is selected ) = 15/100 = 0.15

P(package 3 is selected ) = 30/100 = 0.3

P(package 4 is selected ) = 40/100 = 0.4

P(package 5 is selected ) = 10/100 = 0.1

clearly, we see that all the probabilities differ from one another according to the actual experiment of 100 samples.

So, the data does not confirm the belief that one design is just as likely to be selected by a consumer as any other design.