The Disclaimer
This study was done in an AP Statistics course with
relatively small sample sizes. The
validity of such studies must always be questioned. Please keep this in mind if you use or report the results of this
study.
The Abstract:
For
the past 10 years, people all over the nation have taken time out of their busy
lives every Thursday night and laughed. The cast of Friends have been entertaining
viewers ever since the first episode aired in 1994. The show has been a major
influence in many lives and has definitely made their mark in TV history as
being one of the most popular shows ever. The end of Friends has caused a lot
of talk among the public. Contributing to this, KTLA.com has conducted a poll
asking: “Who is your favorite Friends character?”
Each
of the six characters is different. Monica is the controlling one, Ross is the
smart one, Chandler is the joker, Joey is the clueless one, Phoebe is ditzy,
and Rachel is the outgoing one. Everybody has their own opinion of which one
they like the most. The goal is to determine if there is enough evidence to
support the hypothesis that the distribution of Tates Creek High School seniors
that like each character is the same as the national poll.
A random sample of forty seniors from Tates Creek High School (TCHS) was taken from the population of TCHS seniors who watch Friends and surveyed to determine their favorite character. Once all the data was collected, a chi-squared goodness of fit test was performed. This showed how the votes for each character for the seniors compared to how the nation polled. The results are explained in more detail further on.
Methodology:
This study has been done to
answer the following question: Is there enough evidence to support the
hypothesis that the distribution of TCHS seniors that like each character is the same as the national
poll? The poll conducted by KTLA.com was used as the national reference.
To
perform this study, a simple random sample of 30 seniors at TCHS was needed. To
achieve this, a roster of all 337 TCHS seniors was obtained. Each student was
given a number, 1 through 337. Then, using the random integer generator on a
TI-83 Plus graphing calculator, eighty numbers were chosen. Each number chosen
was matched with the corresponding name on the roster.
The
survey began once eighty seniors were chosen and recorded on paper. By going
straight down the list, the students were asked if they watched the television
show Friends on a regular basis. If the answer was yes, they were given a
survey and asked to circle which character was their favorite. If the student answered no, they were not given
the release form and not included in the survey. Only thirty seniors were
needed for the survey but eighty were chosen at random in case some of them did
not watch Friends. Once thirty answers were gathered, the rest of the names on
the list were not used. The poll was tallied and the results recorded. After
that, a chi-squared goodness of fit test was performed to determine if there is
enough evidence to support the hypothesis.
Data
|
|
Monica |
Joey |
Ross |
Rachel |
Chandler |
Phoebe |
|
Participant #1 |
|
X |
|
|
|
|
|
Participant #2 |
|
|
|
|
|
X |
|
Participant #3 |
|
X |
|
|
|
|
|
Participant #4 |
|
X |
|
|
|
|
|
Participant #5 |
|
|
|
X |
|
|
|
Participant #6 |
|
|
|
|
X |
|
|
Participant #7 |
X |
|
|
|
|
|
|
Participant #8 |
|
X |
|
|
|
|
|
Participant #9 |
|
|
|
|
|
X |
|
Participant #10 |
|
|
|
|
X |
|
|
Participant #11 |
|
X |
|
|
|
|
|
Participant #12 |
|
|
|
X |
|
|
|
Participant #13 |
|
|
|
|
X |
|
|
Participant #14 |
|
|
|
|
|
X |
|
Participant #15 |
|
|
|
|
X |
|
|
Participant #16 |
|
X |
|
|
|
|
|
Participant #17 |
|
X |
|
|
|
|
|
Participant #18 |
|
X |
|
|
|
|
|
Participant #19 |
|
|
|
X |
|
|
|
Participant #20 |
|
|
|
|
X |
|
|
Participant #21 |
|
X |
|
|
|
|
|
Participant #22 |
|
|
|
X |
|
|
|
Participant #23 |
|
|
X |
|
|
|
|
Participant #24 |
|
|
X |
|
|
|
|
Participant #25 |
|
|
|
X |
|
|
|
Participant #26 |
|
X |
|
|
|
|
|
Participant #27 |
|
|
|
X |
|
|
|
Participant #28 |
|
|
X |
|
|
|
|
Participant #29 |
|
|
X |
|
|
|
|
Participant #30 |
|
|
X |
|
|
|
|
Totals |
1 |
10 |
5 |
6 |
5 |
3 |
|
|
|
|
|
|
|
|
Thirty TCHS seniors answer the
following question: Which Friends
character is your favorite?
National Poll
(According to KTLA.com)
|
Rachel |
Ross |
Monica |
Chandler |
Joey |
Phoebe |
|
335 |
55 |
72 |
246 |
356 |
141 |
TCHS Seniors’ Favorite Character
Rachel
|
Ross |
Monica |
Chandler |
Joey |
Phoebe |
|
6 |
5 |
1 |
5 |
10 |
3 |
Assumptions:
1. All expected values are greater than 1 – This assumption has been met and this is easily proven by looking at the table below.
2. No more than 20% of expected counts are less than 5 – This assumption has been met and looking at the table below also easily proves this.
Hypotheses:
Ho: The distribution of seniors at TCHS that like each character is not different from the national poll distribution (according to KTLA.com).
Ha: The distribution of seniors at TCHS that like each character is different than the national poll distribution (according to KTLA.com).
National Survey
|
|
Monica |
Joey |
Rachel |
Chandler |
Phoebe |
Ross |
|
|
# of votes |
72 |
356 |
335 |
246 |
141 |
55 |
|
|
% of votes |
5.98 |
29.54 |
27.8 |
20.41 |
11.7 |
4.56 |
|
TCHS Seniors Survey
|
|
Monica |
Joey |
Rachel |
Chandler |
Phoebe |
Ross |
|
Observed: |
1 |
10 |
6 |
5 |
3 |
5 |
|
% |
3.33 |
33.33 |
20 |
16.67 |
10 |
16.67 |
|
Expected: 30 * (10*%of votes) |
1.794 |
8.862 |
8.34 |
6.123 |
3.51 |
1.368 |
|
x^2comp. (O-E)^2/E |
.35141 |
.14613 |
.65655 |
.20597 |
.0741 |
9.6429 |
x^2: .35141+.14613+.65655+.20597+.0741+9.6429
= 11.07706
df: 6-1=5
p-value: .04987
Conclusion:
Because the p-value is .04987, which rounded up is the .05 which is the same as alpha equals .05, one has to fail to reject Ho. This means that there is not statistically significant evidence to reject the claim that the distribution of TCHS seniors that like each character is not different from that of the national poll.
It is important to remember that this study had a small sample size with the possibility of undercoverage bias. As you can see, this report is not perfect. There is room for improvement so please keep in mind these factors when analyzing this study.