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Association between Gender and Favorite TV Shows

Association between Gender and Favorite TV Shows. By Emily and Jenny AP Statistics, Period 4. 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.

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Association between Gender and Favorite TV Shows

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  1. Association between Gender and Favorite TV Shows By Emily and Jenny AP Statistics, Period 4

  2. 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.

  3. TV Shows • Family Guy • House • Desperate Housewives • SportsCenter • Grey’s Anatomy • Entourage • One Tree Hill • 24 • Heroes • Friends

  4. Expected Shows for Each Gender Males Females • Family Guy • Sports Center • Entourage • House • 24 • Friends • Grey’s Anatomy • Desperate Housewives • One Tree Hill • Heroes

  5. 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

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

  7. 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.

  8. 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.

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

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

  11. 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.

  12. 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

  13. 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 • 2/166=.0120 • 1/166=.0060

  14. 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

  15. Observed Values: Matrix A

  16. Expected Values: Matrix B

  17. 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

  18. 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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