by emily and jenny ap statistics, period 4 people surveyed females: 95 total males: 103 total total:...

Association between Gender and Favorite TV Shows

By Emily and JennyAP Statistics, Period 4

People SurveyedFemales: 95 totalMales: 103 totalTotal: 198 people were surveyedEach person was instructed to choose up to 3

TV shows on our list of 10 shows, plus an “other” category.

The shows were chosen based on a Facebook statistic list of top ten shows in the PHS network. The survey was a SRS of all PHS students found throughout the school.

TV Shows Family GuyHouseDesperate

HousewivesSports CenterGrey’s Anatomy

EntourageOne Tree Hill24HeroesFriends

Expected Shows for Each GenderMales FemalesFamily GuySports CenterEntourageHouse24

FriendsGrey’s AnatomyDesperate HousewivesOne Tree Hill Heroes

Male ResponsesFamily Guy: 40Sports Center:38House: 26Entourage: 2324: 17 Friends: 12Heroes: 5Desperate Housewives: 2Grey's Anatomy: 2One Tree Hill: 1Other:72

Total: 238 responses166 responses for

the ten shows72 “other”Most Popular Male

“others”-Sopranos -9-Simpsons-5-The Office-5-Lost-4-South Park-3

Female ResponsesFriends: 40Grey's Anatomy: 33House: 24Family Guy: 22Desperate Housewives:

13One Tree Hill: 1224: 10Entourage: 9Heroes: 8Sports Center: 3Other: 67

Total: 241 responses174 responses for

the ten shows67 “other”Most popular female

“other”s-Sex and the City- 5-Scrubs-5-The OC-4-Lost-4-The Hills-3

The Chi-square test of Association/IndependenceWe chose to use this test because we have

two categorical samples (gender and TV show).

Chi-Square test is the overall test for comparing any number of population proportions.

Step 1: State HypothesisNull Hypothesis (Ho): There is no

relationship between gender and favorite TV show.

Alternate Hypothesis (Ha): There is an association between gender and favorite TV show.The shows that are expected for each gender

will have proportions of p=.19 or more, and the shows that are not expected for each gender will have p=.01 or less.

Male Expected ValuesMale Shows: 166(.19)= 31.54

Female Shows: 166(.01)= 1.66

Family Guy HouseEntourageSports Center24

Grey’s AnatomyOne Tree HillDesperate HousewivesHeroesFriends

Female Expected ValuesFemale shows: 174(.19)= 33.06

Male Shows: 174(.01)= 1.74

Grey’s AnatomyOne Tree HillDesperate HousewivesHeroesFriends

Family Guy HouseEntourageSports Center24

Step 2: Choose an Inference Procedure and Verify ConditionsCheck that all expected values are at least 1

and no more than 20% are less than 5.Since more than 20% of our expected values

are less than 5 we will proceed with caution.

Step 3: Carry Out the Selected ProcedureTo do the Chi-Square test we put all of the

Observed Values into Matrix A and all of the Expected Values into Matrix B. Our Matrices were 10X2 because there were ten TV shows and two genders. We then used our calculators to carry out the test.

X^2= sum of (observed-expected)^2/expected

Male Observed ProportionsTV Show ProportionFamily Guy:Sports Center:House:Entourage:24:Friends:Heroes:Desperate Housewives:Grey's Anatomy: One Tree Hill:

40/166 =.241038/166 =.228926/166 =.156623/166 =.138617/166 =.102412/166=.07235/166=.03012/166 =.01202/166=.01201/166=.0060

Female Observed ProportionsTV Shows ProportionsFamily Guy:Sports Center:House:Entourage:24:Friends:Heroes:Desperate Housewives:Grey's Anatomy: One Tree Hill:

22/174= .12643/174= .017224/174=.13799/174= .051710/174 =.057540/174= .22998/174= .046013/174= .074733/174= .189712/174= .0690

Observed Values: Matrix ATV Show Male Female

Family Guy 40 22

Sports Center 38 3

House 26 24

Entourage 23 9

24 17 10

Friends 12 40

Heroes 5 8

Desperate Housewives

2 13

Grey’s Anatomy 2 33

One Tree Hill 1 12

Expected Values: Matrix BTV Show Males Females

Family Guy 31.54 1.74

Sports Center 31.54 1.74

House 31.54 1.74

Entourage 31.54 1.74

24 31.54 1.74

Friends 1.66 33.06

Heroes 1.66 33.06

Desperate Housewives

1.66 33.06

Grey’s Anatomy 1.66 33.06

One Tree Hill 1.66 33.06

Chi-Square Test for Association/IndependenceAfter Plugging in Matrices A and B on

calculator for the χ2 –test we found:χ2= 103.5935P=2.9453E^-18=.00000000000000000295df=(10-1)(2-1)=(9)(1)=9

Step 4: Interpret your Results in ContextSince the P-value is extremely small, we can

reject the null hypothesis and accept the alternative hypothesis. This means that there is an association between gender and favorite TV show.