Obs SAT 333 110 322 176 236 264 279 235 258 360 57 268 162 298 344 126 255 252 107 110 105 90 150 83 197 343 221 331 81 256 169 152 285 192 91 97 GPA 1220 1250 1240 1350 1420 1280 1360 1340 1200 990 1260 1340 1470 1140 1130 1120 1270 1200 1370 1250 1350 1140 1130 1040 1420 1140 1190 1260 1280 1040 1250 1200 920 1380 1140 1200 Piercings 3.01 3.33 3.18 2.4 3.4 3.73 4 3.85 3.45 3.27 3.3 3.2 3.69 2.9 3.25 2.2 2.87 3.6 2.9 3.33 2.8 2.7 2.9 3.25 3.6 3.3 3.5 2.9 3.4 3.3 3.05 2.72 2.8 3.8 2.8 3.1 1 Sample size 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 36 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 3.01 3.33 3.18 2.4 3.4 3.73 4 3.85 3.45 3.27 3.3 3.2 3.69 2.9 3.25 2.2 2.87 3.6 2.9 3.33 2.8 2.7 2.9 3.25 3.6 3.3 3.5 2.9 3.4 3.3 3.05 2.72 2.8 3.8 2.8 3.1 0 1 3.100435 3.343846 0.243411 3.01 1, 3.33 0, 3.18 0, 2.4 0, 3.4 0, 3.73 0, 4 1, 3.85 1, 3.45 0, 3.27 1, 3.3 1, 3.2 0, 3.69 1, 2.9 1, 3.25 0, 2.2 0, 2.87 0, 3.6 0, 2.9 0, 3.33 0, 2.8 0, 2.7 0, 2.9 1, 3.25 1, 3.6 1, 3.3 0, 3.5 0, 2.9 0, 3.4 0, 3.3 0, 3.05 0, 2.72 0, 2.8 1, 3.8 1, 2.8 0, 3.1 1, (GPA) =1.77+0.0012(SAT) QUESTIONS 1. Using appropriate software (can use excel and the free online software called statkey), produce a scatterplot of GPA against SAT score using the sample. Compute the sample correlation and comment on the degree of association between the two variables. (There is no need to show your computational steps.) 2. Test whether there is a statistically significant linear association between GPA and SAT score, showing all your steps and clearly stating your conclusion. You are curious whether, in terms of GPA, students with body piercings perform worse than students without any piercing, on average. 3. Set up the null and alternative hypotheses taking care to define your notation clearly. 4. Using Statkey with the 'reallocate groups' randomization method, produce a dotplot of the randomization distribution (with at least 2,000 samples) of the appropriate sample statistic. Carry out the hypothesis test using the randomization distribution and state your conclusion. 5. Verify that the Central Limit Theorem applies in this case, carry out the same hypothesis test using the appropriate approximation and state your conclusion. Briefly compare these results to your findings in question 4. 3 To further evaluate whether GPA is a linear function of SAT score, you decide to set up an appropriate regression model. 6. Write down your regression model taking care to define your notation clearly. Using appropriate software, estimate the regression model and report your results. 7. Use your regression results to give a one-sentence interpretation of the regression slope estimate. 8. Test whether SAT score is an effective predictor of GPA in the regression model you have estimated in question 6. Make sure you report your null and alternative hypotheses, the test statistic, decision rule, and conclusion to the test. 9. Briefly comment on the relationship between your results for the sample correlation test in question 2 and the regression model test in question 8. 1. Is SAT the y-axis or GPA? sample correlation=0.357 The two variables, namely GPA and SAT have a weak positive association 2. n=36 degrees of freedom=n-2=36-2=34 2(0.0069)=0.0138 1.38%>1% 1.38 is higher than our given significance level so there is no statistically significant linear association between GPA and SAT score 3. H0: 1 HA: 1 Where = 2 < 2 4. 1 2 is the mean number of GPA of students with body piercings is the mean number of GPA of students without body piercings p=0.954 As 95.4%>1% there is little evidence that the mean GPA of students with body piercing is less that students without 95 seems very high, do you think its right? 5. The central limit theorem applies as the data is not too skewed, and our n=36 which is larger than 30, also there are more than 10 students who do not and do have a body piercing. I do not know how to do the rest of this question. 6. I'm confused, should SAT be in the y-axis or GPA, do I need to show or do anything else? regression line ^ =877.294+110.624(GPA) SAT regression line ^ =1.77+0.0012(SAT) GPA 7. for every one point increase in GPA you can expect the SAT score to increase by an average of 110.624 points for every one point increase in SAT you can expect the GPA to increase by an average of 0.0012 points 8. H0: 1 HA: 1 =0 0 b1=0.00115 t1=(b1-null)/SE1=(110.624-0)/0.00052=212738.467 Please help me finish this question. 9. Please help me with 9 too DATA (full data is on the excel file) SAT,GPA 1220,3.01 1250,3.33 1240,3.18 1350,2.4 1420,3.4 1280,3.73 1360,4 1340,3.85 1200,3.45 990,3.27 1260,3.3 1340,3.2 1470,3.69 1140,2.9 1130,3.25 1120,2.2 1270,2.87 1200,3.6 1370,2.9 1250,3.33 1350,2.8 1140,2.7 1130,2.9 1040,3.25 1420,3.6 1140,3.3 1190,3.5 1260,2.9 1280,3.4 1040,3.3 1250,3.05 1200,2.72 920,2.8 1380,3.8 1140,2.8 1200,3.1