A researcher is interested in knowing whether showing the video "The Plea" to a group of prosecutors reduces their use of plea bargaining. She takes a sample of 8 prosecutors and finds out how many cases out of the last ten they plea bargained before watching the video and after the video. Produce a research and null hypothesis and test the null hypothesis at the .05 level of significance.

Prosecutor	Before Watching Video	After Watching Video
1	8	6
2	3	4
3	9	3
4	10	9
5	4	4
6	5	8
7	8	9
8	7	3

a. Note a research and null hypothesis in symbols.

b. Calculate degrees of freedom and identify your critical value for t.

c. Test your null hypothesis doing the math by hand. You must show your work for each step! (Hint: You must calculate the standard deviation for distribution of before-after difference scores first, then standard error of the mean difference, then t).

d. Can you reject your null hypothesis? How do you know?

e. What can you conclude?