A survey by Ipsos-Reid reported in American Demographics showed that if a person

Question

A survey by Ipsos-Reid reported in American Demographics showed that if a person was given a $1,000 windfall, 36% would spend the money on home improvement, 24% on leisure travel/vacation, 15% on clothing, 15% on home entertainment or electronic products, and 10% on local entertainment including restaurants and movies. Suppose a researcher believes that these results would not be the same if posed to adults between 21 and 30 years of age. The researcher conducts a new survey interviewing 200 adults between 21 and 30 years of age asking these same questions. A chi-square goodness-of-fit test is conducted to compare the results of the new survey to the one taken by Ipsos- Reid. The Excel results follow. The observed and expected values are for the categories as already listed and appear in the same order. Discuss the findings. How did the distribution of results from the new sur- vey compare to the old? Discuss the business implica- tions of this outcome.

21-30 Years of Age General Population Observed Expected 72 42 30 30 The p-value for the chi-square goodness-of-fit test is: 0.0000043. The observed chi-square for the goodness of fit test is: 30.27.

Explanation / Answer

We have to test the null hypothesis

H0: phome=0.36, pleisure=0.24,pclothing=0.15,pentertainment=0.15

Versus the alternative hypothesis

Ha: phome0.36 or pleisure0.24 or pclothing0.15 or pentertainment0.15

For this chi-square test of goodness of fit is applied and the results showed that all categories have expected count greater than 5, so assumption of chi-square test is satisfied. We have enough evidence to reject the null hypothesis 2(4)=30.27, p=0.0000043<0.05. Hence at least on proportion is different from hypothesized for money posed to adults between 21 and 30 years of age. So business implication is that the amount spent on these things may differ and should focus on different proportions.

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