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# Hypothesis

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A company that depends heavily on advertising for selling its products wants to know if its various advertising media have different effectiveness relative to the age of the customer. The company uses its warranty return cards to collect the following information:
This is a table that lists type of advertisement first then it is broken out in age groups with totals at the end.

Type of Ages
Ad 21-30 31-40 41-50 Over 50 Totals

Store Display 21 28 8 6 63
Catalog 8 5 1 1 15
Magazine 1 23 8 1 33
Newspaper 18 14 2 4 38
Totals 48 70 19 12 149

a. Set up the hypotheses to test whether type of advertisement and age of customer are independent.

b. What population will the test apply to?

c. Calculate the expected frequencies for each cell.
d. How many degrees of freedom will the test have?

e. Without collapsing any cells, calculate the value of the chi-square test statistic.

f. At the 0.05 level of significance, are type of advertisement and age of customer independent?

g. Do you think that categories should have been collapsed? Why or why not?

h. What categories would you recommend collapsing to fix the problem?

#### Solution Preview

A company that depends heavily on advertising for selling its products wants to know if its various advertising media have different effectiveness relative to the age of the customer. The company uses its warranty return cards to collect the following information:
This is a table that lists type of advertisement first then it is broken out in age groups with totals at the end.

Table 1 ( We denote the values by Xi)

Type of Ages
Ad 21-30 31-40 41-50 Over 50 Totals

Store Display 21 28 8 6 63
Catalog 8 5 1 1 15
Magazine 1 23 8 1 33
Newspaper 18 14 2 4 38
Totals 48 70 19 12 149

a. Set up the hypotheses to test whether type of advertisement and age of customer are independent.

Solution. The ...

#### Solution Summary

The expert examines the hypothesis testing for advertising products.

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