Question

TechX have received complaints of excessive packaging of one of their products.  To test whether new minimalist packaging is preferred and whether the proportion of people who prefer the new packaging is different for different age groups, they have conducted a market test of the new packaging.  The results are given in the table below:

Age Group	less than 20	20 to 40	over 40	total
Prefer New Packaging	108	108	84
Prefer Old Packaging	54	75	71
Total

(a) At a 5 % significance level is the proportion of people who prefer the new packaging the same for all age groups?  Set up and test the appropriate hypotheses.

(b) Suppose that a person is chosen at random from the people in the table above.  If you know that the person chosen is < 20, what is the probability that he/she prefers the new packaging?

Answer 1

Using SPSS:

Make variables in Variable View.

Now Click on Values then give the lables in Age Group Variable:

Write 1 in Value and level name of Age Group in Lables.

Now Click on Values then give the lables in Packaging Variable:

Now Enter data in Data View:

Now Weight the Frequency of data:

Steps: Data-->Weight Cases

Select the Freq variable in Frequency Variable then click to ok.

Now Use Chi-square test:

Steps: Analyze-->Basic Statistics-->Crosstabs

Select Packaging in Rows and Age Group in Columns then click on Statistics:

Then tick the Chi-square and Click to Ok and Continue.

Output:

That is the Cross table.

Here, Chi-Square = 5.251, degree of freedom = 2 and P-value = 0.072.

Where p-value is 0.072, that is greater than 0.05, it is mean there is no association between Age Group and Packaging.