Attempting to motivate customers to make early payment of bills, the manager of a consulting company offered customers an incentive to make early payment, a 20% discount for bills paid within 30 days of issuance of the bill. In order to assess the effect of the new policy on time to payment, the manager sampled 15 accounts and recorded the number of days to payment for the last bill issued under the old system and the first bill issued under the incentive system. The data, in days, are shown in the accompanying table: Bill Old System Incentive 1 92 28 2 88 30 3 65 29 4 85 85 5 95 29 6 64 28 7 65 26 8 62 29 9 90 88 10 89 30 11 65 70 12 75 30 13 84 27 14 90 92 15 80 29
Attempting to motivate customers to make early payment of bills, the manager of a consulting company offered customers an incentive to make early payment, a 20% discount for bills paid within 30 days of issuance of the bill. In order to assess the effect of the new policy on time to payment, the manager sampled 15 accounts and recorded the number of days to payment for the last bill issued under the old system and the first bill issued under the incentive system. The data, in days, are shown in the accompanying table:
|
Bill |
Old System |
Incentive |
|
1 |
92 |
28 |
|
2 |
88 |
30 |
|
3 |
65 |
29 |
|
4 |
85 |
85 |
|
5 |
95 |
29 |
|
6 |
64 |
28 |
|
7 |
65 |
26 |
|
8 |
62 |
29 |
|
9 |
90 |
88 |
|
10 |
89 |
30 |
|
11 |
65 |
70 |
|
12 |
75 |
30 |
|
13 |
84 |
27 |
|
14 |
90 |
92 |
|
15 |
80 |
29 |
a). At 5% level of significance, is there sufficient evidence to conclude that the incentive system is, on the average, effective? Your conclusion must be in terms of the P-Value. Show all necessary work.
b). What type of error is possible and describe this error in terms of the problem.
c). Construct a 95% confidence interval for the difference in the actual average number of days to payment between the two systems. Using this
d). Interpret this interval estimation.
e). Explain the sampling design in this problem. Can you propose another type of sampling design (if any) that could be used to perform the analysis of parts (a) and (c)? Give one advantage and one disadvantage of the design you are proposing. Explain carefully.
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