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By Emily and Jenny AP Statistics, Period 4

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People Surveyed Females: 95 total Males: 103 total Total: 198 people were surveyed Each 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.

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TV Shows Family Guy House Desperate Housewives Sports Center Greys Anatomy Entourage One Tree Hill 24 Heroes Friends

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Expected Shows for Each Gender Males Females Family Guy Sports Center Entourage House 24 Friends Greys Anatomy Desperate Housewives One Tree Hill Heroes

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Male Responses Family Guy: 40 Sports Center:38 House: 26 Entourage: 23 24: 17 Friends: 12 Heroes: 5 Desperate Housewives: 2 Grey's Anatomy: 2 One Tree Hill: 1 Other:72 Total: 238 responses 166 responses for the ten shows 72 other Most Popular Male others -Sopranos -9 -Simpsons-5 -The Office-5 -Lost-4 -South Park-3

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Female Responses Friends: 40 Grey's Anatomy: 33 House: 24 Family Guy: 22 Desperate Housewives: 13 One Tree Hill: 12 24: 10 Entourage: 9 Heroes: 8 Sports Center: 3 Other: 67 Total: 241 responses 174 responses for the ten shows 67 other Most popular female others -Sex and the City- 5 -Scrubs-5 -The OC-4 -Lost-4 -The Hills-3

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The Chi-square test of Association/Independence We 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.

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Step 1: State Hypothesis Null 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.

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Male Expected Values Male Shows: 166(.19)= 31.54 Female Shows: 166(.01)= 1.66 Family Guy House Entourage Sports Center 24 Greys Anatomy One Tree Hill Desperate Housewives Heroes Friends

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Female Expected Values Female shows: 174(.19)= 33.06 Male Shows: 174(.01)= 1.74 Greys Anatomy One Tree Hill Desperate Housewives Heroes Friends Family Guy House Entourage Sports Center 24

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Step 2: Choose an Inference Procedure and Verify Conditions Check 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.

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Step 3: Carry Out the Selected Procedure To 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

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Male Observed Proportions TV Show Proportion Family Guy: Sports Center: House: Entourage: 24: Friends: Heroes: Desperate Housewives: Grey's Anatomy: One Tree Hill: 40/166 =.2410 38/166 =.2289 26/166 =.1566 23/166 =.1386 17/166 =.1024 12/166=.0723 5/166=.0301 2/166 =.0120 1/166=.0060

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Female Observed Proportions TV Shows Proportions Family Guy: Sports Center: House: Entourage: 24: Friends: Heroes: Desperate Housewives: Grey's Anatomy: One Tree Hill: 22/174=.1264 3/174=.0172 24/174=.1379 9/174=.0517 10/174 =.0575 40/174=.2299 8/174=.0460 13/174=.0747 33/174=.1897 12/174=.0690

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Observed Values: Matrix A TV ShowMaleFemale Family Guy4022 Sports Center383 House2624 Entourage239 241710 Friends1240 Heroes58 Desperate Housewives213 Greys Anatomy233 One Tree Hill112

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Expected Values: Matrix B TV ShowMalesFemales Family Guy31.541.74 Sports Center31.541.74 House31.541.74 Entourage31.541.74 2431.541.74 Friends1.6633.06 Heroes1.6633.06 Desperate Housewives1.6633.06 Greys Anatomy1.6633.06 One Tree Hill1.6633.06

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Chi-Square Test for Association/Independence After Plugging in Matrices A and B on calculator for the χ2 –test we found: χ2= 103.5935 P=2.9453E^-18=.00000000000000000295 df=(10-1)(2-1)=(9)(1)=9

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Step 4: Interpret your Results in Context Since 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.

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