Week 8 Application Assignment (16 Points)

HYPOTHESIS TESTS COMPARING TWO POPULATIONS

Problem 1) OSU FOOTBALL (5 pts)

News of your analytical prowess has spread throughout the country.Naturally, when the coaching staff of OSU's football team has a statistical question, they contact the best: you.The coaching staff wants to know if they can be 95% confident that the average difference between OSU and their opponent is more than two touchdowns (14 points).Use the data below from 30 randomly chosen games to answer their question.OSU's scores are listed first.

44 - 28

42 - 13

14 - 17

28 - 3

28 - 14

49 - 7

38 - 10

49 - 28

34 - 27

38 - 12

20 - 13

38 - 0

42 - 24

42 - 20

42 - 35

59 - 0

42 - 28

42 - 27

31 - 24

49 - 37

55 - 14

31 - 24

56 - 17

52 - 24

50 - 28

66 - 0

21 - 35

34 - 17

35 - 40

24 - 34

Step 1) What type of hypothesis test is required here?______

How would you run this test in MINITAB (Menus, Functions used)?

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

Step 2) Verify all assumptions required for this test:

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

Null hypothesis

Alternate hypothesis

Step 4) Run the correct test in MINITAB and provide the information below.Use correct symbols and round answers to 3 decimal places.

Test Statistic= Degrees of freedom=

Critical Value= p-value=

Step 5) State your statistical decision (and justify it!)

Step 6) Interpret your decision within the context of the problem: what is your conclusion?

Problem 2) FIREFLIES (6 pts)

Your hard work building the fancy fire pit you saw on Pinterest has really paid off! Now every weekend evening in the summer your neighbors and their kids come over to enjoy conversation, games, and cool beverages with you and your family.One especially cunning parent has managed to convince the neighborhood children to put down their tablets and phones and play by catching (and sometimes releasing) fireflies.You make a game out of it by seeing how many they can catch every 15 minutes.Throughout the course of a long evening you collect the data below, which shows how many fireflies the kids catch every 15 minutes.Assuming this data comes from a normally distributed population - can you conclude that the average number of fireflies caught after 10pm was greater than the average caught before 10pm?Use = 0.05.

Before 10pm

After 10pm

8:00

8:15

8:30

8:45

10:00

10:15

10:30

10:45

6

8

12

9

15

12

9

14

9:00

9:15

9:30

9:45

11:00

11:15

11:30

11:45

8

13

11

10

10

12

8

10

Step 1) What type of hypothesis test is required here?

How would you run this test in MINITAB (Menus, Functions used)?

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

Step 2) Verify all assumptions required for this test:

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

Null hypothesis

Alternate hypothesis

Step 4) Run the correct test in MINITAB and provide the information below.Use correct symbols and round answers to 3 decimal places.

Test Statistic= Degrees of freedom=

Critical Value= p-value=

Step 5) State your statistical decision (and justify it!)

Step 6) Interpret your decision within the context of the problem: what is your conclusion?

Problem 3) HIGH SCHOOL REUNION (5 pts)

As Senior Class President, one of your lifelong duties is overseeing the planning of your high school reunions.Your cross-town high school rivals had their reunion a month ago and 63 of their 413 alumni attended.You and your team added some extra events and lowered the cost to encourage more people to attend, and for your reunion you had the same number of attendees, but your graduating class only had 327 students.Using a 90% confidence level, can you accurately claim that your class had a higher attendance rate than your cross-town rivals?

Step 1) What type of hypothesis test is required here?

How would you run this test in MINITAB (Menus, Functions used)?

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

Step 2) Verify all assumptions required for this test:

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

Null hypothesis

Alternate hypothesis

Step 4) Run the correct test in MINITAB and provide the information below.Use correct symbols and round answers to 3 decimal places.

Test Statistic=

Critical Value=

p-value= _______

Step 5) State your statistical decision (and justify it!)

Step 6) Interpret your decision within the context of the problem: what is your conclusion?