Is there a difference in preference for free-range eggs across age groups? In order to develop marketing strategies, egg suppliers are interested in what type of customers only bought eggs produced in...

Is there a difference in preference for free-range eggs across age groups? In order to develop marketing strategies, egg suppliers are interested in what type of customers only bought eggs produced in either free-range or caged conditions. Surveys were conducted at multiple retail outlets. The results are summarised in the table below.

a) When testing a null hypothesis of no association between the two factors in this contingency table, what would be the contribution to the test statistic from the ‘Caged and Below 30’ cell?

b) Is there any evidence from this data that type of eggs bought is related to age group? Provide appropriate hypotheses, decision rule and conclusion for this test at the 5% significance level based on a test statistic of 8.999. Address any assumptions or necessary conditions in your analysis. If you find evidence of an association between the variables, describe it.

c) Use this data to construct a 90% confidence interval for the proportion of this population who only buy caged eggs. Provide a meaningful interpretation of your interval.