Hypothesis with two populations

Franklin University
Math 280 – Introduction to Probability and Statistics
Name: _____________________
Module 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. [This data set is provided in an Excel file on the assignment page]
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?
______
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 using a software and provide the information below. Use correct symbols
and round answers to 3 decimal places.
Test Statistic
=
Degrees of freedom
=
Critical Value
=
p-value
=
1
081020
Franklin University
Math 280 – Introduction to Probability and Statistics
Name: _____________________
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 (5 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 𝛼 = 0.05. [The data set is in the Excel file on the assignment page]
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?
Is this a left-tailed, right-tailed, or two-tailed test?
Step 2) Verify all assumptions required for this test:
2
081020
Franklin University
Math 280 – Introduction to Probability and Statistics
Name: _____________________
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 using a software 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 (6 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?
Step 2) Verify all assumptions required for this test:
3
081020
Franklin University
Math 280 – Introduction to Probability and Statistics
Name: _____________________
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 using a software 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?
4
081020