Question

The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in high-crime areas of Miami, Florida, are being examined to test the effectiveness of the program. The difference in crimes reported is calculated as (crimes after - crimes before). You want to test whether the crimes reported before is less than those reported after and, thus, the hypotheses are as follows: Null Hypothesis: ?_D ? 0, Alternative Hypothesis: ?_D < 0. You perform a paired sample t-test and see a p-value of 0.9633. What is the appropriate conclusion?

Question 13 options:

1)	The average difference in crimes reported is significantly less than 0. The average number of crimes reported was higher before the program.

2)	We did not find enough evidence to say there was a significantly positive average difference in crimes reported. The program does not appear to have been effective.

3)	We did not find enough evidence to say there was a significantly negative average difference in crimes reported. The program does not appear to have been effective.

4)	We did not find enough evidence to say the average difference in crimes reported was not 0. The program does not appear to have been effective.

5)	The average difference in crimes reported is greater than or equal to 0.

Answer 1

We reject H₀ if p-value is less than level of significance.

In this case p-value is very high i.e. 0.9633. This means we do not reject H₀ and reject the alternative hypothesis, i.e., the average difference is negative. This means the program does not appear to have been effective. Hence, the answer is

3)  We did not find enough evidence to say there was a significantly negative average difference in crimes reported. The program does not appear to have been effective.