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# Analyses of Survey’s Statistics

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### Analyses of Survey’s Statistics

1. 1. Analyses of Survey’s Statistics<br />Griselda Escobedo<br />Jessica DeLuna<br />Avigail Carrillo<br />Mr. Eastvedt, Period 4<br />
2. 2. Survey Questions Administered to Baldwin Park High School Students:<br />1. Male/Female<br />2. Age<br />3. Are you single? Y/N<br />4. If your partner cheated on you would you react violently? Y/N<br />5. Do you like Justin Bieber? Y/N<br />6. Do you believe in God? Y/N<br />7. Have you ever cut class? Y/N<br />8. How many years older than you would you date someone? (#)<br />9. How many children do you want? (#)<br />10. On a scale of 1-10, how important is the color of a car to you? (10 being the highest)<br />
3. 3. Confidence Intervals<br />Equation for numerical questions: <br />Sample mean ± 1.96 (σ/√n) <br />One can be 95% confident that the population mean is contained within that interval. <br />Equation for opinion questions (proportions): <br />p hat = proportion of “Yes” answers<br />q hat= 1 – p hat = proportion of “No” answers<br />p hat ± 1.96√[(p hat∙q hat)/n]<br />One can be 95% confident that the interval will contain the population proportion. <br />
4. 4. Confidence intervals for the means of numerical questions:<br />Q8: 5.339 ± 1.230 <br />We are 95% confident that the true mean of accepted age difference is between 4.109 and 6.569. <br />Q9: 5.273 ± 2.741<br />We are 95% confident that the true mean of children wanted is between 2.532 and 8.014. <br />Q10: 6.567 ± 0.577<br />We are 95% confident that the true mean of the scaled importance of car color is between 5.990 and 7.144.<br />
5. 5. Confidence intervals for opinion questions (Y/N proportion): <br />Q3: 0.618 ± 0.101 <br />We are 95% confident that the population proportion of single individuals is within the interval (0.517, 0.719).<br />Q4: 0.146 ± 0.073 <br />We are 95% confident that the population proportion of violent reactions to infidelity is within the interval (0.073, 0.219).<br />Q5: 0.178 ± 0.079 <br />We are 95% confident that the population proportion of Justin Bieber fans is within the interval (0.099, 0.257)<br />
6. 6. Proportion confidence intervals continued.. <br />Q6: 0.862 ± 0.072 <br />We can be 95% confident that the population proportion is within the interval (0.790, 0.934).<br />Q7: 0.544 ± 0.103 <br />We can be 95% confident that the population proportion is within the interval (0.441, 0.647).<br />
7. 7. Question 6: Hypothesis Test on Larger Study<br />“The survey finds that the number of people who say they are unaffiliated with any particular faith today (16.1%)..” http://religions.pewforum.org/reports<br />The results of our survey administered to Baldwin Park High School show that 13 out of 87 (≈15%) of the students do not believe in God. <br />1. H0: p=.161 <br /> Ha: p≠.161<br /> n=87 <br />2. Assumptions/Conditions:<br /> Randomness: The sample was randomly selected. <br /> 10% condition: The sample is less than 10% of the population. <br /> We may assume the data is evenly distributed. <br />3. We will conduct a 1-proportion z-test <br />4. P hat= 0.150 z=(.150-.161)/√[(.161)(.839)/87]= -0.279<br />P-value is ≈ 0.3897<br />5. Since the p-value is significantly greater than 0.05, we may not reject the null hypothesis. There is not enough evidence to suggest that there is a significant difference between the proportion of atheists. <br />
8. 8. Question 7: Hypothesis Test on Larger Study<br />“The high dropout rate may also be related to the finding that half of the respondents said they have skipped school..” http://newsinfo.iu.edu/web/page/normal/4948.html<br />The results of our survey reveal that 40 out of 89 students (≈50%) have cut class before. <br />1. H0: p=.50 <br />Ha: p≠.50<br />n=89<br />2. Assumptions/Conditions:<br /> Randomness: The sample was randomly selected. <br /> 10% condition: The sample is less than 10% of the population. <br /> We may assume the data is evenly distributed. <br />3. We will conduct a 1-proportion z-test <br />4. P hat= 0.50 z=(.50-.50)/√[(.50(.50/89]= 0 <br />P-value is .5000 <br />With such a high p-value, we cannot reject the null hypothesis. Therefore we may conclude that the proportions of students that have skipped school are equal. <br />
9. 9. Comparing the means of affirmative responses for males vs. females<br />Question 8: How many years older than you would you date someone? <br />1. H0: MeanM= MeanF ; Ha: MeanM≠ MeanF; Mean= mean yrs. difference<br />2. -Randomness: Survey sample was acquired randomly.<br /> -Independence: The age of one student does not affect another’s.<br /> -10% condition: The 87 students are less than 10% of the population. <br /> -Nearly normal: The distributions are nearly normal. <br />3. We will conduct a 2 sample T-test. <br />4. nM=46 nF=41 XM=3.707 XF=7.171 sM=4.786 sF=6.524 df=85 <br /> t= (XM-XF)/[√(sM2/nM)+(sF2/nF)] = -2.795 <br /> p= 0.006414<br />5. Since the p-value is less than 0.05, we can reject the null hypothesis; there is enough evidence to suggest that mean years-difference accepted by males is different from that of females. <br />
10. 10. Comparing the means of affirmative responses for males vs. females<br />Question 9: How many children do you want? <br />H0: MeanM= MeanF; Ha: MeanM≠ MeanF; Mean= mean children wanted<br />2. -Randomness: Survey sample was acquired randomly.<br /> -Independence: The age of one student does not affect another’s.<br /> -10% condition: The 88 students are less than 10% of the population. <br /> -Nearly normal: The distributions are nearly normal. <br />We will conduct a 2 sample T-test.<br />nM=47 nF=41 XM=3.957 XF=6.780 sM=6.032 sF=18.231 df=86 <br /> t= (XM-XF)/[√(sM2/nM)+(sF2/nF)] = -0.947<br /> p=0.346292<br />5. Since the p-value is less than 0.05, we may reject the null hypothesis that the mean children wanted by males is equal to that of females; there is enough evidence to prove that the difference is significant. <br />
11. 11. Comparing the means of affirmative responses for males vs. females<br />Question 10: On a scale of 1-10, how important is the color of a car to you? (10 being the highest)<br />H0: MeanM= MeanF ; Ha: MeanM≠ MeanF; Mean= mean scale <br />2. -Randomness: Survey sample was acquired randomly.<br /> -Independence: The age of one student does not affect another’s.<br /> -10% condition: The 89 students are less than 10% of the population. <br /> -Nearly normal: The distributions are nearly normal. <br />3. A 2 sample T-test will be conducted.<br />4. nM=48 nF=41 XM=7.115 XF=5.927 sM=2.610 sF=2.893 df=87 <br /> t= (XM-XF)/[√(sM2/nM)+(sF2/nF)] = 2.020<br /> p=0.046460<br />5. There is enough evidence against the null hypothesis since the p-value is less than 0.05. We may conclude that the importance of a car’s color is different among males vs. females and reject the null hypothesis. <br />
12. 12. Chi2 Tests to determine whether grade levels have different opinions. <br />Equation: <br />X2= ∑ [ (O – E )2 / E ]<br />where O is the observed value, and E is the expected value. <br />
13. 13. Chi2 Test<br />Question 4: If your partner cheated on you would you react violently?<br />H0: Reacting violently is independent of age. <br />Ha: Reacting violently is not independent of age. <br /> Observed: Expected:<br />X2=1.075 P=0.898 df=4<br />Since the p-value is greater than 0.05, we do not reject the null hypothesis. We may conclude that reaction violently is independent of age. <br />
14. 14. Chi2 Test<br />Question 5: Do you like Justin Bieber? <br />H0: Having a positive regard of Justin Bieber is independent of age. <br />Ha: Having a positive regard of Justin Bieber is not independent of age. <br /> Observed: Expected: <br />X2 =7.787 P=0.010 df=4<br />At the 0.05 significance level we may reject the null hypothesis and conclude that liking Justin Bieber is dependent on age. <br />
15. 15. Chi2 Test<br />Question 6: Do you believe in God? <br />H0: Believing in God is independent of age. <br />Ha: Believing in God is not independent of age. <br /> Observed: Expected:<br />X2=5.208 P=0.267 df=4 <br />With such a high p-value, at the 0.05 level of significance the null hypothesis may not be rejected. Therefore we conclude that the belief in God is independent of age. <br />
16. 16. Chi2 Test<br />Question 7: Have you ever cut class? <br />H0: Having ever cut class is independent of age. <br />Ha: Having ever cut class is not independent of age. <br /> Observed: Expected:<br />X2=5.165 P=0.271 df=4 <br />Since the p-value is greater than 0.05, we may not reject the null hypothesis and conclude that cutting class is independent of age. <br />