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A survey by Ipsos-Reid reported in American Demographics showed that if a person was given a $1,000 wind-fall, 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 Europeans. The researcher conducts a new survey interviewing 200 randomly selected European adults asking these same questions. A chi-square goodness-of-fi t test is conducted to compare the results of the new survey to the one takenbyIpsos-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 survey compare to the old? Discuss the business implications of this outcome.

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Got Milk? Researchers Sharon Peterson and Madeleine Sigman-Grant wanted to compare the overall nutrient intake of American children (ages 2 to 19) who exclusively use skim milk instead of 1%, 2%, or whole milk. The researchers combined children who consumed 1% or 2% milk into a “mixed milk” category. The following data represent the daily calcium intake (in mg) for a random sample of eight children in each category and are based on the results presented in their article “Impact of Adopting Lower-Fat Food Choices on Nutrient Intake of American Children,” Pediatrics, Vol. 100, No. 3.

(a) Is there sufficient evidence to support the belief that at least one of the means is different from the others at the  level of significance? Note: The requirements for a one-way ANOVA are satisfied.

(b) If the null hypothesis is rejected in part (a), use Tukey’s test to determine which pairwise means differ using a familywise error rate of

(c) Draw boxplots of the three categories to support the analytic results obtained in parts (a) and (b).

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Rates of Return A stock analyst wondered whether the mean rate of return of financial, energy, and utility stocks differed over the past five years. He obtained a simple random sample of eight companies from each of the three sectors and obtained the five-year rates of return shown in the following table (in percent):

(a) State the null and alternative hypotheses.

(b) Verify that the requirements to use the one-way ANOVA procedure are satisfied. Normal probability plots indicate that the sample data come from normal populations.

(c) Are the mean rates of return different at the  level of significance?

(d) Draw boxplots of the three sectors to support the results obtained in part (c).

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According to an extensive survey conducted for  Marketing by Leo J. Shapiro & Associates, 66% of all computer companies are going to spend more on marketing this year than in previous years. Only 33% of other information technology companies and 28% of non-information technology companies are going to spend more. Suppose a researcher wanted to conduct a survey of her own to test the claim that 28% of all non-information technology companies are spending more on marketing next year than this year. She randomly selects 270 companies and determines that 62 of the companies do plan to spend more on marketing next year. Use 0.05, the chi-square goodness-of-fit test, and the sample data to test to determine whether the 28% figure holds for all non-information technology companies.

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