1. Statistical Analyses of the Sexual Ideologies of BPHS Students Cristian Castillo George Damian Steven Do

2. Confidence Intervals for Means Question 2: Age X = 16.80, n = 87, df = 86, t* = 1.663, s = 0.696 16.80 ± 1.663 * (0.696/(sqrt87)) = (16.652, 16.948) We are 95% confident that the true mean age of survey participants is between 16.652 and 16.948 years.

3. Confidence Intervals for Means Question 3: Grade Level X = 11.43, n = 83, df = 82, t* = 1.664, s = 1.270 11.43 ± 1.664 * (1.270/(sqrt83)) = (11.153, 11.707) We are 95% confident that the true mean grade level of survey participants is between 11.153 and 11.707.

4. Confidence Intervals for Means Question 4: Number of times engaged in unprotected sex (in the past year) X = 1.012, n = 83, df= 82, t* = 1.664, s = 2.652 1.012 ± 1.664 * (2.652/(sqrt83)) = (.4329 , 1.591) We are 95% confident that the true mean of the number of times a survey participant engaged in unprotected sex in the past year is between .4329 and 1.591.

5. Confidence Intervals for Means Question 5: Number of sexual partners in the past year X = 1, n = 83, df = 82, t* = 1.664, s = 1.807 1 ± 1.664 * (1.807/(sqrt83)) = (.6054, 1.395) We are 95% confident that the true mean number of sexual partners that a survey participant has had in the past year is between .6054 and 1.395.

6. Confidence Intervals for Means Question 6: Number of times in a day where one thinks about sex X = 3.104, n = 67, df= 66, t* = 1.668, s = 5.216 3.104 ± 1.668 * (5.216/(sqrt67)) = (1.831, 4.376) We are 95% confident that the true mean number of times in a day when a survey participant thinks about sex is between 1.831 and 4.376.

7. Confidence Intervals for Proportions Question 1: Gender p = 0.414, q = 0.586, z* = 1.960, n = 83 0.414 ± 1.960 * sqrt[(.414)(.586)/(87)] = (0.310, 0.517) We are 95% confident that the true proportion of affirmative (male) participants is between .310 and .517.

8. Confidence Intervals for Proportions Question 7: Abortion p = 0.409, q = 0.591, z* = 1.960, n = 83 0.409 ± 1.960 * sqrt[(.409)(.591)/(83)] = (0.303, 0.515) We are 95% confident that the true proportion of affirmative responses (agreement to the method of abortion) is between .303 and .515.

9. Confidence Intervals for Proportions Question 8: Abstinence p = 0.479, q = 0.521, z* = 1.960, n = 73 0.479 ± 1.960 * sqrt[(.479)(.521)/(73)] =(0.364, 0.594) We are 95% confident that the true proportion of affirmative responses (for the concept of abstinence) is between .364 and ,594.

10. Confidence Intervals for Proportions Question 9: Adoption if one cannot raise a newborn p = 0.90, q = 0.10, z* = 1.960, n = 80 0.90 ± 1.960 * sqrt[(.90)(.10)/(80)] = (0.834, 0.966) We are 95% confident that the true proportion of affirmative responses (the concept of putting a child up for adoption if one does not possess adequate qualities to raise it) is between .834 and .966.

11. Confidence Intervals for Proportions Question 10: Raising a newborn p = .833, q = .167, z* = 1.960, n = 84 0.833 ± sqrt[(.833)(.167)/(84)] = (0.753, 0.913) We are 95% confident that the true proportion of affirmative responses (raising a newborn if it was your bearing) is between .753 and .913.

12. Hypothesis Test (Larger Study) Question 7: Abortion “A new Gallup Poll, conducted May 7-10, finds 51% of Americans calling themselves "pro-life" on the issue of abortion and 42% "pro-choice.”” We do not know whether or not the study was conducted randomly, but there is no reason not to assume the sample as unrepresentative.1 Our sample of responses to the concept of abortion showed that 34 out of the 83 respondents claimed a pro-choice point view.

13. Hypothesis Test (Larger Study) Question 7: Abortion H0: p = .51 Ha: p ≠ .51 n = 83 2. Randomness: Survey sample was acquired at random. 10% condition: The sample consisted of less than 10% of the population. np = 83(.51) = 42.33 > 10 nq = 83(.49) = 40.67 > 10 3. We will conduct a 1-proportion z-test. 4. ˆp = .410 z = .410-.51/sqrt[(.51)(.49)/83] = -1.83 p = 0.0674 5. Since the p-value greater than .05, we do not reject the null hypothesis. There is not enough evidence to say that the proportion of the pro-life opinions on abortion in the Gallup poll differ from our sample of pro-life opinions.

14. Hypothesis Test (Larger Study) Question 8: Abstinence “Over 50 percent of teens chose to be abstinent, and abstinence is becoming more popular. 73 percent of teens say they do not think it is embarrassing for a teen to be a virgin, and 58 percent say teens should not have sex, regardless of what precautions they take…” Randomness is not stated, but there is no reason to assume otherwise.2 Our sample of responses to the concept of abstinence showed that 35 out of the 73 respondents claimed a pro-abstinence point view.

15. Hypothesis Test (Larger Study) Question 8: Abstinence H0: p = .58 Ha: p ≠ .58 n = 73 2. Randomness: Survey sample was acquired at random. 10% condition: The sample consisted of less than 10% of the population. np = 73(.58) = 42.34 > 10 nq = 73(.42) = 30.66 > 10 3. We will conduct a 1-proportion z-test. 4. ˆp = .479 z = .479-.58/sqrt[(.58)(.42)/73] = -1.74 p = 0.082 5. Since the p-value greater than .05, we do not reject the null hypothesis. There is not enough evidence to say that the proportion of the pro-abstinence opinions on teenhelp.com differ from our sample of pro-abstinence opinions.

16. Hypothesis Test Comparing Affirmative Responses (Males vs. Females) Question 2: Age H0: MeanM = MeanF ; Ha: MeanM ≠ MeanF MeanM = Mean age of males MeanF = Mean age of females 2. Randomness: Survey sample was acquired randomly. Independence: Age of one individual does not affect another’s. 10% condition: 36 males and 51 females are less than 10% of the population. Nearly normal: Distributions are nearly normal with no outliers. (See next slide) 3. We will conduct a 2-sample t-test. 4. nM=36, xM=16.81, sM=0.668; nF=51, xF=16.82, sF=0.713; df = 85 P(t ≠ (16.81 – 16.82)/sqrt[(0.6682/36 + 0.7132/51)] t = 0.0669, p = 0.947 5. Since the p-value is much greater than .05, we have no conclusive evidence against the null hypothesis. There is no difference between the mean age of males and females within the sample.

17. Hypothesis Test Comparing Affirmative Responses (Males vs. Females) Question 2: Age

18. Hypothesis Test Comparing Affirmative Responses (Males vs. Females) Question 3: Grade Level H0: MeanM = MeanF ; Ha: MeanM ≠ MeanF MeanM = Mean grade level of males MeanF = Mean grade level of females 2. Randomness: Survey sample was acquired randomly. Independence: One individual’s grade level does not affect another’s. 10% condition: 36 males and 47 females are less than 10% of the population. Nearly normal: Male distribution is skewed left while female distribution is roughly symmetric. (See next slide) 3. We will conduct a 2-sample t-test. 4. nM=36, xM=11.555, sM=0.558; nF=47, xF=11.574, sF=0.499; df = 81 P(t ≠ (11.555– 11.574)/sqrt[(0.5582/36 + 0.4992/47)] t = -0.160, p = 0.872 5. Since the p-value is greater than .05, we have no conclusive evidence against the null hypothesis. There is no difference between the mean grade level s of males and females within the sample.

19. Hypothesis Test Comparing Affirmative Responses (Males vs. Females) Question 3: Grade Level

20. Hypothesis Test Comparing Affirmative Responses (Males vs. Females) Question 4: Number of times engaged in unprotected sex (in the past year) H0: MeanM = MeanF ; Ha: MeanM ≠ MeanF MeanM = Mean number of times males had unprotected sex in the past year MeanF = Mean number of times females had unprotected sex in the past year 2. Randomness: Survey sample was acquired randomly. Independence: Aside from partnership within the sample, the number of times one chooses to have unprotected sex does not affect another’s. 10% condition: 34 males and 49 females are less than 10% of the population. Nearly normal: Both distributions are skewed to the right. (See next slide) 3. We will conduct a 2-sample t-test. 4. nM=34, xM=1.353, sM=3.374; nF=49, xF=0.775, sF=2.013; df = 81 P(t ≠ (1.353– 0.775)/sqrt[(0.3.3742/34 + 2.0132/49)] t = 0.895, p = 0.375 5. Since the p-value is greater than .05, we have insufficient evidence against the null hypothesis. There is no difference between the mean number of times a male/female had unprotected sex in the past year.

21. Hypothesis Test Comparing Affirmative Responses (Males vs. Females) Question 4: Number of times engaged in unprotected sex (in the past year)

22. Hypothesis Test Comparing Affirmative Responses (Males vs. Females) Question 5: Number of sexual partners (in the past year) H0: MeanM = MeanF ; Ha: MeanM ≠ MeanF MeanM = Mean number of sexual partners males had in the past year MeanF = Mean number of sexual partners females had in the past year 2. Randomness: Survey sample was acquired randomly. Independence: Aside from partnership within the sample, the number of partners one chooses to engage in sex with does not affect another’s. 10% condition: 34 males and 49 females are less than 10% of the population. Nearly normal: Both distributions are skewed to the right. (See next slide) 3. We will conduct a 2-sample t-test. 4. nM=34, xM=1.706, sM=2.541; nF=49, xF=0.510, sF=0.739; df = 81 P(t ≠ (1.706– 0.510)/sqrt[(2.5412/34 + 0.7392/49)] t = 2.667, p = 0.0113 5. Since the p-value is less than .05, we conclude that there is sufficient evidence against the null hypothesis. We reject the claim that the mean number of sex partners a male had in the past year is equal to the mean number of sex partners a female had in the past year.

23. Hypothesis Test Comparing Affirmative Responses (Males vs. Females) Question 5: Number of sexual partners (in the past year)

24. Hypothesis Test Comparing Affirmative Responses (Males vs. Females) Question 6: Number of times a day one thinks about sex H0: MeanM = MeanF ; Ha: MeanM ≠ MeanF MeanM = Mean number of times a day males think about sex MeanF = Mean number of times a day females think about sex 2. Randomness: Survey sample was acquired randomly. Independence: The number of times a day one individual thinks about sex does not affect another’s. 10% condition: 28 males and 39 females are less than 10% of the population. Nearly normal: Male distribution is bimodal while female distribution is skewed right. (See next slide) 3. We will conduct a 2-sample t-test. 4. nM=28, xM=5.393, sM=5.852; nF=39, xF=1.462, sF=4.038; df = 65 P(t ≠ (5.393– 1.462)/sqrt[(5.8522/28 + 4.0382/39)] t = 3.068, p = 0.00364 5. Since the p-value is less than .05, we can conclude that there is sufficient evidence against the null hypothesis. We reject the claim that the mean number of times a day males thinks about sex is equal to the mean number of times a day females think about sex.

25. Hypothesis Test Comparing Affirmative Responses (Males vs. Females) Question 6: Number of times a day one thinks about sex

26. x2 Test for Homogeneity Among Grades Question 7: Abortion

27. x2 Test for Homogeneity Among Grades Question 7: Abortion Ho: Affirmative responses (agree) to the concept of abortion are independent of grade level. Ha: Affirmative responses to the concept of abortion are dependent on grade level. Randomness: Survey sample was selected at random. 10% condition: We sampled less than 10% of the world’s population of high school students. We will conduct a x2 test for homogeneity. X2 = (0-0.384)2/0.384 + (0-0.57)2/0.57 + (1-0.047)2/0.047 + (11-12.66)2/12.66 + (20-18.80)2/18.80 + (2-1.54)2/1.54 + (22-19.95)2/19.95 + (29-29.63)2/29.63 + (1-2.42)2/2.42 = 21.99 P = .000201 Since the P-value is less than .05, we proceed to reject the null hypothesis. There is not enough evidence to suggest that the affirmative responses regarding the concept of abortion are independent of grade level.

28. x2 Test for Homogeneity Among Grades Question 8: Abstinence

29. x2 Test for Homogeneity Among Grades Question 8: Abstinence H0: Affirmative responses (for) to the concept of abstinence are independent of grade level. Ha: Affirmative responses to the concept of abstinence are independent of grade level. Randomness: Survey sample was selected at random. 10% condition: We sampled less than 10% of the world’s population of high school students. We will conduct a x2 test for homogeneity. X2 = (0-0.402)2/0.402 + (0-0.425)2/0.425 + (1-0.172)2/0.172 + (12-13.28)2/13.28 + (14-14.03)2/14.03 + (7-5.69)2/5.69 + (23-21.32)2/21.32 + (23-22.52)2/22.52 + (7-9.14)2/9.14 = 5.866 P = 0.209 Since the p-value is greater than .05, it is concluded that there is insufficient evidence against the null hypothesis. We do not reject the hypothesis that affirmative responses to the concept of abstinence are independent of grade levels.

30. x2 Test for Homogeneity Among Grades Question 9: Adoption if one cannot raise a newborn

31. x2 Test for Homogeneity Among Grades Question 9: Adoption if one cannot raise a newborn Ha: Affirmative responses (agree) to the idea of adoption if one cannot raise a newborn are independent of grade level. H0: Affirmative responses to the idea of adoption if one cannot raise a newborn are dependent of grade level. Randomness: Survey sample was selected at random. 10% condition: We sampled less than 10% of the world’s population of high school students. We’ll conduct a x2 test for homogeneity. X2 = (0-0.839)2/0.839 + (0-0.092)2/0.092 + (1-0.069)2/0.069 + (25-28.53)2/28.53 + (5-3.13)2/3.13 + (4-2.35)2/2.35 + (48-43.63)2/43.63 + (3-3.13)2/3.13 + (1-3.59)2/3.59 = 19.194 P = .000719 Since the p-value is less than .05, we proceed to reject the null hypothesis. There is insufficient evidence to conclude that affirmative responses toward the idea of putting a child up for adoption is independent of grade level.

32. x2 Test for Homogeneity Among Grades Question 10: Raising a newborn

33. x2 Test for Homogeneity Among Grades Question 10: Raising a newborn Ha: Affirmative responses (for) toward the idea of raising a newborn if one were to impregnate/be impregnated are independent of grade level. H0: Affirmative responses toward the idea of raising a newborn if one were to impregnate/be impregnated are dependent of grade level. Randomess: Survey sample was selected at random. 10% condition: We sampled less than 10% of the world’s population. We’ll conduct a x2 test for homogeneity. X2 = (0-0.779)2/0.779 + (0-0.186)2/0.186 + (1-0.035)2/0.035 + (29-26.48)2/26.48 +(4-6.33)2/6.33 + (1-1.19)2/1.19 + (38-39.73)2/39.73 + (12-9.48)2/9.49 + (1-1.78)2/1.78 = 29.87 P = .0000052 Since the p-value is lower than .05, we will proceed to reject the null hypothesis. There is not enough evidence to conclude that affirmative responses to the idea of raising a newborn if one were to impregnate/be impregnated are

34. References 1"More Americans-Pro-Life - Than-Pro-Choice-€ for First Time." Gallup.Com - Daily News, Polls, Public Opinion on Government, Politics, Economics, Management. Web. 25 May 2011. <http://www.gallup.com/poll/118399/more-americans-pro-life-than-pro-choice-first-time.aspx>. 2"Benefits of Teen Abstinence - Teen Sexuality." Teen Help - Advice for Parents and Teens. Web. 26 May 2011. <http://www.teenhelp.com/teen-sexuality/teen-abstinence.html>.