Part 1) GETTING THE SCOOP (6 points)

News of your analytical prowess has spread throughout the area.Naturally, when the coaching staff of your teen's high school lacrosse team has a statistical question, they contact the best, you.The coaching staff wants to know if the average difference between the home team and their opponent is more than +2 points.Use the data below from 35 randomly chosen games to answer their question using = 0.01.The home team's scores are listed first.

12 - 6

7 - 5

10 - 4

5 - 6

9 - 8

7 - 5

7 - 2

8 - 6

8 - 2

8 - 4

7 - 1

8 - 5

6 - 4

13 - 5

10 - 4

5 - 8

9 - 6

6 - 5

5 - 4

10 - 6

7 - 10

14 - 10

7 - 2

6 - 5

6 - 5

7 - 6

8 - 7

8 - 3

9 - 8

8 - 6

10 - 4

10 - 9

6 - 7

8 - 1

8 - 5

1.What is the name of the type of hypothesis test required here?

Is this a left-tailed, right-tailed, or two-tailed test?

2.State AND verify all assumptions required for this test.

3.State the null and alternate hypotheses for this test: (use correct symbols and format!)

Null hypothesis

Alternate hypothesis

4.Run the correct hypothesis test and provide the information below.Give the correct symbols AND numeric value of each of the following (round answers to 3 decimal places).

Test Statistic

Critical value [HINT: this is NOT ]

Degrees of Freedom

p-value

5.State your statistical decision (and justify it!) and interpret your decision within the context of the problem. What is your conclusion?