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Homework answers / question archive / 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)
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.
Given that
N Mean SD
October 2001 1000 $2411 $847.43
October 2000 1000 $2814 $976.93
The null hypothesis under consideration is
H0: There is no significant difference in the mean credit card debt of October 2001 & October 2000
H1: The mean credit card debt of October 2001 is significantly lower than that of & October 2000
Test Statistic
where
Rejection Criteria: Reject the null hypothesis if the calculated value is less than the critical value of t at 0.05 level of significance.
Details
Calculated value of t = -9.8541
Critical value = -1.64515
P value = 0.0000
Conclusion: Reject the null hypothesis as the calculated value of t is less than the critical value. Also the p value is less than the significance level. Thus the claim that consumers are trying to reduce their credit card debt can be accepted.
Confidence Interval
The 95 % Confidence interval for the difference of credit card debt of October 2001 & October 2000 is given by
where and
The 95 % CI is given by
[-483.2043 , -322.7957]
With 95 % confidence we can conclude that the difference in the mean credit card debt of October 2001 & October 2000 will be in the interval [-483.2043 , -322.7957]
please see the attached file.
