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 confirm the belief that one design is just as likely to be selected as another? Explain.

Design	Number of Design Times Preferred
1	5
2	15
3	30
4	40
5	10

Answer 1

There are 5 designs, if one design is just as likely to be selected by a consumer as any other design, then we expect equal probability for each design selection

Probability (p) = 1/(number of designs) = 1/5 = 0.20

selection probability assigned to each of the package designs is 0.20

Expected value = n*p = 100*0.2 = 20

Hypotheses for this test are

Ho: Preference is same for all designs.

H1: Preference is not same for all desgins.

Given values are observed frequencies

Test statistic calculation

Degree of freedom = number of designs -1 = 5-1 = 4

Using chi square distribution table with test statistic 42.5 and df(4)

we get

p value = 0.0000 < significance level 0.05

So, we will reject the null hypothesis.

Conclusion:- We have insufficient evidence to conclude that one design is just as likely to be selected as another.