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 greater 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 0.0487. What is the appropriate conclusion?

Question 9 options:

1) The average difference in crimes reported is significantly different from 0. There is a significant difference in crimes reported due to the program.

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

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

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

5) 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.

Answer 1

The null and alternative hypotheses for the given paired t test are given as below:

Null hypothesis: H₀: Average number of crimes reported before the special program is less than or same as the average number of crimes reported after the special program.

Alternative hypothesis: H_a: Average number of crimes reported before the special program is greater than the average number of crimes reported after the special program.

For this paired t test, P-value is given as 0.0487 (approx. 0.05) which is greater than the level of significance or alpha value of 0.01 or 0.02 and it is approximately equal to the default significance level of alpha value of 0.05; so we do not reject the null hypothesis that Average number of crimes reported before the special program is less than or same as the average number of crimes reported after the special program.

There is insufficient evidence to conclude that Average number of crimes reported before the special program is greater than the average number of crimes reported after the special program.

Correct Answer:

5) 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.