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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 Summary

The expert examines the hypothesis testing for advertising products.

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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.

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 ...

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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