TechX have received complaints of excessive packaging of one oftheir products.  To test whether new minimalist packagingis preferred and whether the proportion of people who prefer thenew packaging is different for different age groups, they haveconducted a market test of the new packaging.  Theresults 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 whoprefer the new packaging the same for all agegroups?  Set up and test the appropriate hypotheses.
(b) Suppose that a person is chosen at random from the people inthe table above.  If you know that the person chosen is< 20, what is the probability that he/she prefers the newpackaging?
