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 after is greater than those reported before and, thus, the hypotheses are as follows: Null Hypothesis: μ_D ≤ 0, Alternative Hypothesis: μ_D > 0. You perform a paired sample t-test and see a p-value of 0.5155. What is the appropriate conclusion?

Question 16 options:

1)	The average difference in crimes reported is less than or equal to 0.

2)	The average difference in crimes reported is significantly larger than 0. The average number of crimes reported was higher after the program.

3)	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.

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)	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.

Answer 1

The Decision Rule is that if p value is < Alpha, then Reject H0.

Although Alpha is not mentioned, the p value is very large, which means that the probability of getting a test statistic as large as or greater than the one obtained, assuming that the null is true is very high. Therefore, we fail to reject the null hypothesis.

Hence Option 3: 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.