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According to a survey conducted in October, 2001, consumers were trying to reduce their credit card debt (Margaret Price, "Credit Debts Get Cut Down to Size," Newsday, November 25, 2001, F3)

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According to a survey conducted in October, 2001, consumers were trying to reduce their credit card debt (Margaret Price, "Credit Debts Get Cut Down to Size," Newsday, November 25, 2001, F3). Based on a sample of 1,000 consumers in October 2001 and in October 2000, the mean credit card debt was $2,411 in October 2001 as compared to $2,814 in October 2000. Suppose that the standard deviation was $847.43 in October 2001 and $976.93 in October 2000.

a) Assuming that the population variances from both years are equal, is there evidence that the mean credit card debt is lower in October 2001 than in October 2000? (use =0.05 level of significance).
b) Find the p-value in (a) and interpret its meaning.
c) Assuming that the population variances from both years are equal, construct and interpret a 95 % confidence interval estimate of the difference between the population means in October 2001 and October 2000.