Paired samples t-test for the given data.
A local voluntary organization affiliated to the Citizens Advice Bureau offers free financial advice to residents in the area who are registered debtors. In order to see how effective the service is, 15 randomly selected clients were monitored and their initial debts, and those after 6 months of counseling were recorded. These data are exhibited in table. You may assume that initial debts and those after 6 months of counseling are both normally distributed and have equal variances.
Undertake a paired samples test on these data to establish, at the 5% significance level, if there was an overall reduction in debt, on average, after receiving financial advice from the voluntary organization. You must provide the hypotheses for this test and a clear statement of your findings.
|
Initial debt
|
Debt after 6 months
|
|
5865.9
|
5681.4
|
|
6911.4
|
6382.5
|
|
8325.9
|
7895.4
|
|
9297.6
|
9580.5
|
|
9113.1
|
7907.7
|
|
8252.1
|
8301.3
|
|
7034.4
|
7083.6
|
|
10478.4
|
10220.1
|
|
8325.9
|
7624.8
|
|
9715.8
|
9137.7
|
|
7784.7
|
7920.0
|
|
10503.0
|
10097.1
|
|
8461.2
|
7907.7
|
|
8535.0
|
8227.5
|
|
9997.0
|
9991.0
|