You want to know whether police officers who have attended training on use of force use Tasers a fewer number of times during the past year than police officers who have not attended training on use of force. You collect data on use of force incidents for officers who attended training and those who did not. Below is the excel output testing your null hypothesis at .05 level of significance:

	Before	After
Mean	51.16	73.21
Variance	1699.37	7629.11
Observations		318.00
Pooled Variance	4885.35
Hypothesized Mean Difference	0.00
df	590.00
t Stat	-3.83
P(T<=t) one-tail	1.01
t Critical one-tail	-1.65
P(T<=t) two-tail	0.00
t Critical two-tail	-1.96

a. Note a null and research hypothesis in symbols.

b. What is the mean number of use of force incidents among officers who attended training?

c. What is the sample size? How do you know?

d. Note the t critical value that you would use to compare the calculated value of t to.

e. Using the p value from the table, can you reject your null hypothesis? How do you do?

f. Using the t critical value and t calculated value from the table, can you reject your null hypothesis? How do you do?