Question

A matched-pairs t-test was performed to determine the effectiveness of a a financial planning program intended to reduce an individual's monthly debt. The diagrams below illustrate the test statistic and the rejection region for two different levels of significance. What conclusions can be drawn?

-The program was shown to be ineffective at the 5% significance level but effective at the 10% significance levels.
-The program was shown to be effective at both the 5% and the 10% significance levels.
-The program was shown to be ineffective at the 10% significance level but effective at the 5% significance levels.
-The program was shown to be ineffective at both the 5% and the 10% significance levels.
-A conclusion cannot be drawn from these diagrams.

Answer 1

The financial planning program is ineffective at the 5% significance level but effective at the 10% level, as per the matched-pairs t-test statistics compared against critical values.

Step-by-step explanation:

To determine the effectiveness of a financial planning program for reducing monthly debt using a matched-pairs t-test, it is essential to compare the test statistic with the critical value at different levels of significance. If the test statistic falls within the rejection region at a certain significance level, the null hypothesis (that there is no effect) is rejected, indicating the program is effective at that level of significance.

When the test statistic falls within the rejection region at the 10% significance level but not at the 5% significance level, this means that the program is considered effective at the less stringent 10% level (since the data show a statistically significant effect) but not at the more stringent 5% level (which suggests the evidence is not strong enough to show effectiveness).

The correct conclusion is: The program was shown to be ineffective at the 5% significance level but effective at the 10% significance levels.