During 2004 a company implemented a number of policies aimed at reducing the ages of its customers' accounts. In order to assess the effectiveness of these measures, the company randomly selects 10 customer accounts. The average age of each account is determined for the years 2003 and 2004. These data are given in Table 10.5. Assuming that the population of paired differences between the average ages in 2004 and 2003 is normally distributed:
a. Set up the null and alternative hypotheses needed to establish that the mean average account age has been reduced by the company's new policies.
TABLE 10.5
Average Account Ages in 2003 and 2004 for 10 Randomly Selected Accounts

b. Figure 10.11 gives the Excel output needed to test the hypotheses of part a. Use critical values to test these hypotheses by setting a equal to .101 .051 .011 and .001. How much evidence is there that the mean average account age has been reduced?
FIGURE 10.11
Excel Output of a paired Difference Analysis of the Account Age Data

c. Figure 10.11 gives the p-value for testing the hypotheses of part a. Use the p-value to test these hypotheses by setting a equal to .101 .051 .011 and .001. How much evidence is there that the mean average account age has been reduced?
d. Calculate a 95 percent confidence interval for the mean difference in the average account ages between 2004 and 2003. Estimate the minimum reduction in the mean average account ages from 2003 to 2004.

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Average Age of Account in 2003 (Days) 35 24 47 28 Average Age of Account in 2004 Account (Days) 27 19 40 30 2 25 31 29 15 21 35 51 18 28 9 10 t-Test: Paired Two Sample for Means 04 Age 27 53.55556 10 0.804586 03 Age 34 104.2222 10 Mean Variance Observations Pearson Correlation Hypothesized Mean df t Stat P(Tc-t) one-tail t Critical one-tail P(T<-t) Two-tail t Critical two-tail -3.61211 0.00282 1.833114 0.005641 2.262159